Japanese | Math Olympiad Problem | Logarithms Simplification | What is the Value of m = ?
Solve logarithmic equation #logarithms#olympiad
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Пікірлер: 15
Is this the way you teach mathematics? Wonderful?
@superacademy247
Ай бұрын
Thanks 👍💯 for your support
m=1 is the only solution. Experienced students will know this just by looking at the equation. ln(1)/ln(25)-ln(1)/ln(125)=0/ln(25)-0/ln(125)=0-0=0
You could have a much simpler way of solving for m by noting that you already had 2logm 3logm. That will give yo log m = 0; i.e. m = 1.
@leonznidarsic
Ай бұрын
I agree that it often complicates the interpretation of the problem and therefore takes too long to come to a solution
we can write log25(m) as (1/2)log5(m) and log125(m) as (1/3)log5(m). now same base easy 2 steps left.
By looking at the definition of logarithm we find 125^x = 25^x ( = m). This is only true for x=0 and therefore m = 25^0 = 125^0 = 1. Can be solved mentally.
Решение будет 1 минута Если помнить что 25=5^2,125=5^3 и log(a^b) c=(log(a) b) /c Тогда log(5^2)x-log(5^3)x=0 (1/2-1/3)log(5)x=0 x=0
Easy way to solve 1. m should not be equal to zero ( log 0 is undefined (log m)/log 25 - (log m)/125 =0 (log 25 - log 125) × log m = 0 Because log 25 - log 125 is not equal to zero log m = 0 Hence m = 1 Thanks
@superacademy247
Ай бұрын
Thanks for your support and input 👍
@rabotaakk-nw9nm
Ай бұрын
👍, but... /125 -> /log 125 log 25 - log 125 -> 1/log 25 - 1/log 125 or log 125 - log 25
While i admire your great knowledge in log rules the simplest fact has been overlooked here. That is if the logarithm of x on base a is equal to the logaritm of x on a different base b the solution is always x=1 as long as a is not equal to b and a,b >1
@ManjulaMathew-wb3zn
Ай бұрын
loga(x) - logb(x) =0 loga(x) - ( loga(x)/loga(b)) = 0 Loga(x)(1. - 1/loga(b)) = 0 The second term is non zero. Loga(x)=0 x=1
@superacademy247
Ай бұрын
Thanks for your input and support
too much long