Solving Logarithmic Equations With Different Bases - Algebra 2 & Precalculus

This algebra 2 and precalculus video tutorial focuses on solving logarithmic equations with different bases. To do this, you need to understand how to use the change of base formula and how to simplify and evaluate logarithmic expressions. Other techniques that are useful to know includes factoring cubic polynomials by synthetic division, using the rational root theorem, binomial expansion theorem with Pascal's triangle, and a basic knowledge of the properties of exponents. In addition, you need to know how to condense multiple logs into a single logarithmic expression and how to convert an equation from logarithmic form to exponential form.
Logarithms - The Easy Way!
• Logarithms - The Easy ...
Log to Exponential Form:
• Writing Logarithmic Eq...
Change of Base Formula:
• Change of Base Formula...
Change of Base Log Problem:
• Logarithms
Properties of Logarithms:
• Properties of Logarithms
____________________________________
Expanding Logarithmic Expressions:
• Expanding Logarithmic ...
Condensing Logarithmic Expressions:
• Condensing Logarithmic...
Natural Logarithms:
• Natural Logarithms
Solving Exponential Equations:
• Solving Exponential Eq...
Exponential Equations - Quadratic Form:
• Solving Exponential Eq...
_______________________________________
Solving Logarithmic Equations:
• Solving Logarithmic Eq...
Graphing Logarithmic Functions:
• Graphing Logarithmic F...
Graphing Exponential Functions:
• How To Graph Exponenti...
Compound Interest Word Problems:
• Compound Interest
Logarithms Practice Problems:
• Logarithms - Practice ...
_______________________________________
Final Exams and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
/ collections

Пікірлер: 254

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor Жыл бұрын

    Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: kzread.info/dash/bejne/aHemuqivptrZkag.html

  • @user-gq9gm2en4g
    @user-gq9gm2en4g3 жыл бұрын

    i left this video feeling like a math genius, then i opened my assignment question. i cried

  • @rumanmdhasan6224

    @rumanmdhasan6224

    3 жыл бұрын

    Same here,bro!

  • @elshowdeantony

    @elshowdeantony

    3 жыл бұрын

    Frfr

  • @dynamicagi1561

    @dynamicagi1561

    3 жыл бұрын

    😂😂😂

  • @DigiCLIPS283

    @DigiCLIPS283

    3 жыл бұрын

    Lol we all in the same boat....jeez I hate math🤦🏽‍♂️

  • @christabelrewe749

    @christabelrewe749

    2 жыл бұрын

    same

  • @stellaorga
    @stellaorga4 жыл бұрын

    You really saved me. Made me cry when I solved the answer on my own and got it. Thanks a lot

  • @lilmosey5783

    @lilmosey5783

    2 жыл бұрын

    Ur wired

  • @galaxyyy3427

    @galaxyyy3427

    2 жыл бұрын

    @@lilmosey5783 damn they're really wired, so connected

  • @tez817
    @tez8175 жыл бұрын

    Can we swap brains just for this upcoming test???

  • @user-oe4wy2fg3e

    @user-oe4wy2fg3e

    4 жыл бұрын

    I call dibs first!

  • @portiamalefahlo8330

    @portiamalefahlo8330

    3 жыл бұрын

    Please

  • @princessalexander1349
    @princessalexander13495 жыл бұрын

    You're saving lives. it's a powerful thing.

  • @Effortless-escapades

    @Effortless-escapades

    5 жыл бұрын

    Princess Alexander mine is not saved

  • @gourihegde4311

    @gourihegde4311

    4 жыл бұрын

    Princess Alexander really!!

  • @mahderworku7554

    @mahderworku7554

    3 жыл бұрын

    People say Captain America, Ironman he is the real hero

  • @georgesadler7830
    @georgesadler78302 жыл бұрын

    MR. Organic Chemistry Tutor, thank you for Explaining and Solving Logarithmic Equations with Different Bases. Understanding logarithm is very important in all levels of math, engineering, physics, chemistry and all the Enviromental's sciences.

  • @spencer4562
    @spencer45622 жыл бұрын

    You're a key stakeholder in our education 😭❤️🔥

  • @leagueoflivinglegends5913
    @leagueoflivinglegends59135 жыл бұрын

    first time I watched a 32 min math video and not get bored. payed more attention here than in MY CLASS

  • @anthoniamokwunye8511
    @anthoniamokwunye85112 жыл бұрын

    Thanks for all you do. You have really helped me alot. God bless and reward you 🙏

  • @vishugaur6178
    @vishugaur61783 жыл бұрын

    You are a genius man had difficulty in this particular concept and you cleared all ky doubts

  • @elebeonupeter1477
    @elebeonupeter14773 жыл бұрын

    Thank you, this was very helpful in refreshing what I had forgotten.

  • @tmannazy
    @tmannazy3 жыл бұрын

    Beautiful...I've gotten back this log wahala solved through this tutorial. Thanks.

  • @denvercharlebois699
    @denvercharlebois6994 жыл бұрын

    His math tutorials is therapeutic for me.

  • @cindychilufya9220
    @cindychilufya9220 Жыл бұрын

    I used to find it so hard to change bases in secondary school, but now that I'm in college, plus this video, it's a walk over

  • @yazanmarwan8447
    @yazanmarwan84474 жыл бұрын

    Thank you for this very amazing explantion 👍🏻👍🏻

  • @Sultan_A
    @Sultan_A3 ай бұрын

    Very Good, The Organic Chemistry Tutor, Keep It Up 🌟

  • @renewd
    @renewd6 жыл бұрын

    These are lengthy and involved compared to some other logarithm problems, but a good challenge.

  • @harrisonthegr8526
    @harrisonthegr85263 жыл бұрын

    I’m in middle school and I’m taking geometry rn but I figured that if I learned stuff like this I’ll be prepared for the future

  • @uzi6839

    @uzi6839

    3 жыл бұрын

    @@doobiuspoopius2343 yup so tru

  • @broderickproject8721

    @broderickproject8721

    3 жыл бұрын

    Ur smart for doing that, jr year is complete hell. Finals this week, wish me luck

  • @harrisonthegr8526

    @harrisonthegr8526

    3 жыл бұрын

    @@broderickproject8721 just took my final today good luck

  • @noahbenjamin7782

    @noahbenjamin7782

    3 жыл бұрын

    yep finals are hell, definitely helps to be prepared

  • @sunjidasultana4648

    @sunjidasultana4648

    3 ай бұрын

    same here too!

  • @AnilKumar-lv6yf
    @AnilKumar-lv6yf6 жыл бұрын

    Finally helped me to undestand *LOGARITHM* Thanks a lot😊😊

  • @rumanmdhasan6224
    @rumanmdhasan62243 жыл бұрын

    Great video,brother! Those maths seam really easy now!

  • @enriquedevilliers8144
    @enriquedevilliers81442 жыл бұрын

    man thanks brother you seriously help a lot keep doing what you do bro!!!!

  • @CorneliusChilufya
    @CorneliusChilufyaАй бұрын

    This is wonderful and easy to capture the method

  • @josephteweilissah5491
    @josephteweilissah5491 Жыл бұрын

    Perfectly done thank you sir

  • @wistfulgraph
    @wistfulgraph Жыл бұрын

    At 24:58, by skipping over the "non-factorable" quadratic, you skip over a solution which isn't extraneous (because it is a real quadratic and one of the answers fits in the domain necessary for log2(x+3)+log4(5-x)=3. The domain is -3 x>-3 ..... 5-x>0 --> x

  • @The_InsideJoke

    @The_InsideJoke

    Жыл бұрын

    Brain hurty

  • @morganblarue

    @morganblarue

    Жыл бұрын

    Exactly! I didn’t run through the math like you did, but we did leave out another two possible solutions for x (one being negative, so not a solution).

  • @michaels333

    @michaels333

    9 ай бұрын

    Came here for this comment. On the previous problem the quadratic gave complex roots - not the case here

  • @KungFuBarbie-pc7hb

    @KungFuBarbie-pc7hb

    Ай бұрын

    Where'd you get the 1 solution from

  • @bhaktathapa263
    @bhaktathapa263 Жыл бұрын

    This video is really useful. Thank you a lot.

  • @fahembluebluefahem5516
    @fahembluebluefahem55167 жыл бұрын

    very smart method of teaching !! keep going sir ! from an algerian american.

  • @osaijeigbafen6323
    @osaijeigbafen63233 жыл бұрын

    This guy is a life saver

  • @nicholasbathiya3052
    @nicholasbathiya3052 Жыл бұрын

    Kudos to your effort sir.

  • @juliachonarzewski5870
    @juliachonarzewski5870 Жыл бұрын

    This is exactly what I needed

  • @archimedeis
    @archimedeis2 жыл бұрын

    Thank you so much for these.

  • @Chrisymcmb
    @Chrisymcmb4 жыл бұрын

    Thanks m8, I really needed that

  • @myzahra4029
    @myzahra40295 жыл бұрын

    that's helpful , thank you

  • @sskchannelallsubjects4421
    @sskchannelallsubjects44212 жыл бұрын

    Superb fantastic mind-blowing sir

  • @atharvsingh3185
    @atharvsingh31856 жыл бұрын

    Thanks it really helped .....

  • @zekariyasngusu2368
    @zekariyasngusu23683 жыл бұрын

    Thank you this is the best channel

  • @DiyaSewnarain
    @DiyaSewnarain Жыл бұрын

    why are you such a good teacher . i can do my tutorials now lool

  • @theengineeringstudent2678
    @theengineeringstudent26784 жыл бұрын

    So interesting!

  • @gontsekganyago4079
    @gontsekganyago40792 жыл бұрын

    the way everything just links is amazing....i love math...its like an alien language

  • @Devil-dz2jm
    @Devil-dz2jm3 жыл бұрын

    Man, I love your content so damn much

  • @ZakiAsir
    @ZakiAsir4 жыл бұрын

    You are the saint of all students

  • @videolife7264
    @videolife72643 жыл бұрын

    Good explanation and helpful to get the correct idea🔥,Keep doing more🙏

  • @giemar8307
    @giemar83073 жыл бұрын

    Thank you very much Sir..

  • @bonusben3486
    @bonusben34866 жыл бұрын

    have you done a video on solving to x when you have mixed equations of exponentials or logs and normal binomials?

  • @christianayiah9071
    @christianayiah90712 жыл бұрын

    Always best in wat u do

  • @itsss.l
    @itsss.l Жыл бұрын

    He’s just the best ❤❤

  • @keishiekim6111
    @keishiekim61114 жыл бұрын

    You always help me with my maths, thank u so much

  • @hiyashah2335

    @hiyashah2335

    4 жыл бұрын

    oh the british people... mathS lmao

  • @ivashehu7097

    @ivashehu7097

    3 жыл бұрын

    @@hiyashah2335 oh the americans...maaaaaaTH[s] no hard feelings 😂

  • @abrahamekpe3679
    @abrahamekpe36792 жыл бұрын

    Thanks allot at least you have shared your ( maths) knowledge with me

  • @resilientfool7191
    @resilientfool71919 ай бұрын

    So comprehensible yet so mind boggling

  • @GhulamMurtaza-SSGC
    @GhulamMurtaza-SSGC Жыл бұрын

    Thanks 😍😍😍😍 very nice teaching.❤❤

  • @shamusemery3188
    @shamusemery31884 жыл бұрын

    This video was honestly so clutch bro saved me like $40 thank you!

  • @programmingbezaleel
    @programmingbezaleel2 жыл бұрын

    Thank you so much.

  • @herangao4685
    @herangao46855 жыл бұрын

    man u saved me before my test

  • @yasinacademy1145
    @yasinacademy11452 жыл бұрын

    I like ur video it is very helpful

  • @teaaaaa1691
    @teaaaaa16913 жыл бұрын

    THANK YOUUU!!

  • @kevsolomy4768
    @kevsolomy47686 жыл бұрын

    The struggles of IB maths r real!!!

  • @ilhanyusuf2160

    @ilhanyusuf2160

    4 жыл бұрын

    Almostutorials sameee my teacher literally sucks at teaching

  • @aurorg7297

    @aurorg7297

    4 жыл бұрын

    @@ilhanyusuf2160 Same here, we sped through this unit so fast and whenever I ask a question she always gives me a hard time

  • @nadineabdullah9886

    @nadineabdullah9886

    3 жыл бұрын

    i thought this was taught in myp??

  • @anrajsoni2596

    @anrajsoni2596

    3 жыл бұрын

    Auro R'G SAME.

  • @laurenorourke2442
    @laurenorourke24424 жыл бұрын

    Thank you thank you thank you!! I have an algebra 2 quiz tomorrow and i don't understand logarithmic nor exponential equations, so this was really helpful!! Im praying I do well on my quiz tomorrow

  • @simonbawi21

    @simonbawi21

    2 жыл бұрын

    How did you do? You don’t probably remember since it was 1 year ago!

  • @laurenorourke2442

    @laurenorourke2442

    2 жыл бұрын

    @@simonbawi21 i think i actually remember!! i think i got a low A😅 i lowkey miss algebra 2, pre calc kicked my ass last year:(

  • @simonbawi21

    @simonbawi21

    2 жыл бұрын

    @@laurenorourke2442 Thats very good to hear, I'm taking applied calculus in college so I'm just getting help since I don't really learn from lecture.

  • @ImperialAssassi4U
    @ImperialAssassi4U4 ай бұрын

    Hi, is the pre-calculus video playlist in order or is it all mixed? As in, if I wanted to teach myself it would I need to follow the specific order? These videos on Logs come a lot later in the playlist after more complex things like Quotient rule

  • @beverlyfrancis8433
    @beverlyfrancis84334 жыл бұрын

    Thank you.

  • @vashishpersad269
    @vashishpersad2692 жыл бұрын

    you deserve a special spot in heaven. This was amazing thank you :)

  • @mayrasancruz
    @mayrasancruz7 жыл бұрын

    love this! !!

  • @jmmshorts7130
    @jmmshorts71303 жыл бұрын

    Man you are a savior

  • @7sevenAM
    @7sevenAM Жыл бұрын

    i love this guy so much😭😭😭😭😭

  • @serinacat4781
    @serinacat47814 жыл бұрын

    Very helpful thanks haha

  • @thanoswasright2085
    @thanoswasright20853 жыл бұрын

    THANK YOUUUU

  • @Deaxon1
    @Deaxon15 жыл бұрын

    I have an exam today, thanks.

  • @njelekaharriet6107
    @njelekaharriet6107 Жыл бұрын

    OMG I have been failing such kind of question when they come on a test ,but I can't believe that I have known how to solve them

  • @jupiterisalive
    @jupiterisaliveАй бұрын

    thank you

  • @Ioa_kun
    @Ioa_kun2 ай бұрын

    3:52 why did you multiply the right side by 1/3? By the way, you really helped me a lot to catch up in classes, Thanks

  • @hiyashah2335
    @hiyashah23354 жыл бұрын

    ILY LIFE SAVER

  • @vexic2642
    @vexic26424 жыл бұрын

    tysm mate

  • @firayihonese4127
    @firayihonese4127 Жыл бұрын

    No question this guy is a genius

  • @AdityaShinde_11
    @AdityaShinde_113 жыл бұрын

    Wonderful #DefinationsForStudents

  • @zeph8620
    @zeph86204 жыл бұрын

    Can we just exchange everything with Euler's number and use natural log?

  • @nashbrown1725
    @nashbrown17254 жыл бұрын

    bro ur cracked ! da goat im not sus but i luv u right now mwah mwah u save my life by blessing me with this math cant tell u how happy i am rn but u are doing the lords work thank u so much

  • @PhillipClarkePhotography
    @PhillipClarkePhotography6 жыл бұрын

    Thanks Mark Wahlberg!

  • @donotdisturb5127
    @donotdisturb51272 жыл бұрын

    My math exam is in 10 minutes pray for me 😭

  • @rossanadivila

    @rossanadivila

    2 ай бұрын

    You’ll get it.😊

  • @donotdisturb5127

    @donotdisturb5127

    2 ай бұрын

    @@rossanadivila I failed it like 2 years ago lol but ty love

  • @yina6816
    @yina68166 ай бұрын

    @ 21:55 Where (and why) did the multiply both sides with negative one come from?

  • @sohinimishra9202
    @sohinimishra92024 жыл бұрын

    a good vedio

  • @PaleBlueDotCitizen
    @PaleBlueDotCitizen3 жыл бұрын

    @23:37 you stick with x=1 and say there are no other zeros but the quadratic x^2+2x-19 can be solved by completing the square to get x = -1 +/- 2 sqrt 5.

  • @krishhhprj

    @krishhhprj

    2 жыл бұрын

    Nerd jk I’m not that guy

  • @sharonann3259
    @sharonann3259 Жыл бұрын

    rombe nandri ya🙏

  • @kingmonpillay9844
    @kingmonpillay98443 жыл бұрын

    🙏🏽 You're a Math 👼

  • @happyfeet7123
    @happyfeet71234 жыл бұрын

    lmao i love how he just ends the video after the lesson

  • @yatoboy9968

    @yatoboy9968

    2 жыл бұрын

    U wanted him to rap before ending them or smt ? Lol

  • @happyfeet7123

    @happyfeet7123

    2 жыл бұрын

    @@yatoboy9968 there's this thing youtubers and even educational channels do called an "outro" idk if u heard of it but it was kinda cool that this video just didn't have one.

  • @yatoboy9968

    @yatoboy9968

    2 жыл бұрын

    @@happyfeet7123 well the video still awesome with or without that so we do not care bout that unnecessary bs and notice how you're literally the only one rambling about all that junk

  • @happyfeet7123

    @happyfeet7123

    2 жыл бұрын

    @@yatoboy9968 I see you agree with my comment. Good

  • @yatoboy9968

    @yatoboy9968

    2 жыл бұрын

    @@happyfeet7123 bro I was agreeing with you from the start you jus didn't understand me 🐈

  • @thomassidoti5496
    @thomassidoti549623 күн бұрын

    On that problem ending at 24:36 x=1 is a solution and x=-1+2radical(5) is also a solution. If you did the quadratic equation at the end you would have arrived at that. 1-2radical(5) however, is not a solution because it is not in the domain

  • @thomassidoti5496
    @thomassidoti54962 ай бұрын

    Love your videos! in the 2nd to last problem, why aren't 3.472 and -5.472 solutions to the equation? They work out when plugged into the original equation

  • @thomassidoti5496

    @thomassidoti5496

    23 күн бұрын

    3.472 is but not -5.472 because it is not in the domain

  • @roccomelodino4347
    @roccomelodino43474 ай бұрын

    At 22:04 can you explain why you times it by -1 please

  • @Eds3.14
    @Eds3.145 жыл бұрын

    i've been watching your vids for a while and i figured it out... you're a Hispanic with a Boston accent. am i in the ballpark here?

  • @angelan924

    @angelan924

    4 жыл бұрын

    Eduardo Ramirez have you ever seen the movie split ?

  • @afiazaman6622

    @afiazaman6622

    3 жыл бұрын

    @@angelan924 I saw it its great!

  • @ADawg467
    @ADawg4674 жыл бұрын

    when he said two is a factor of 15 by accident I lowkey panicked. ;P

  • @potrkca
    @potrkca6 жыл бұрын

    hi. how do you make a one-off donation to you?

  • @Airborneworms
    @Airborneworms6 ай бұрын

    where are you getting a third from?

  • @user-ny5kv3fy6x
    @user-ny5kv3fy6x8 ай бұрын

    Can I send a question basing on the topic

  • @youssifmansour516
    @youssifmansour5165 жыл бұрын

    Me and my friend are in 6th grade and still love your log,factorials,ln,and algebra vids

  • @wiretrap8007

    @wiretrap8007

    Жыл бұрын

    sweaty tryhard

  • @nathanmofya3866
    @nathanmofya3866 Жыл бұрын

    How can I solve an equation for this sort; 3×10^3+2×10^x+5×10^y=3002.05

  • @briggshightower7959
    @briggshightower79597 жыл бұрын

    Lets assume we have 45 seconds to solve this? How do we get there this quick?

  • @kingston9356

    @kingston9356

    4 жыл бұрын

    You don't

  • @ivashehu7097

    @ivashehu7097

    3 жыл бұрын

    @@kingston9356 😂😂

  • @firayihonese4127

    @firayihonese4127

    Жыл бұрын

    Just guess

  • @anomamirihagalla2870
    @anomamirihagalla28703 жыл бұрын

    120 people unliking this . 😑😑 ok they dont even know what is log 😰😩 this was really helpfull and ots for free

  • @sharannandakumar7809
    @sharannandakumar78092 жыл бұрын

    Bro I have never saw the real god before but hopefully can see you soon 👍👍

  • @mrannunaki6852
    @mrannunaki68526 жыл бұрын

    in the first problem.. after you've changed the bases to logbase3 on both sides can you just cross multiply and solve? cuz its then (logbase3 (x-2)/1) = (logbase3 (4x+7)/3) so.. that = 4x+7 = 3x-6 Then x = -13

  • @simkuntheng5465

    @simkuntheng5465

    6 жыл бұрын

    help me do this one logbase 2 of 2/5=...? logbase 2 of 3/5=...? Thanks!

  • @alexcarter7317

    @alexcarter7317

    4 жыл бұрын

    But the you'll have a negative log value so it won't work.. kinda late but worth mentioning for other readers

  • @mangotango740
    @mangotango7402 жыл бұрын

    what the difference between algebra 2 and precalc?

  • @LuisMartinez-ly8xd
    @LuisMartinez-ly8xd6 жыл бұрын

    where did you got the -1 to multiply into 0= -xCubed - xSquared + 21x - 19(towards the end of the third question)???

  • @LuisMartinez-ly8xd

    @LuisMartinez-ly8xd

    6 жыл бұрын

    time's at 21:48/32:42

  • @PHILLYMEDIC69

    @PHILLYMEDIC69

    5 жыл бұрын

    we dont know man.

  • @nelsonl.barquio2281
    @nelsonl.barquio22813 жыл бұрын

    How to simplify; log2/ log25- log5?

  • @miinjung
    @miinjung2 жыл бұрын

    example - 0:37 ✓ one - 1:49 ✓ two - 14:06 three - 16:45 four - 24:49