SOLUTION: {{{x^log(5,3)=3}}}

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Question 42997This question is from textbook Precalculus
: x%5Elog%285%2C3%29=3 This question is from textbook Precalculus

Found 2 solutions by psbhowmick, Nate:
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
x%5Elog%285%2C3%29=3

Taking the logarithm of both sides w.r.t. base 3
log%283%2Cx%5Elog%285%2C3%29%29=log%283%2C3%29
or log%285%2C3%29%2Alog%283%2Cx%29=1

We can write for a>0 and b>0 log%28a%2Cb%29+=+log%28c%2Ca%29%2Flog%28c%2Cb%29 where c is any number.

or %28log%2810%2C3%29%2Flog%2810%2C5%29%29%2A%28log%2810%2Cx%29%2Flog%2810%2C3%29%29=1

Cancelling log%2810%2C3%29 from both numerator and denominator we have
log%2810%2Cx%29%2Flog%2810%2C5%29=1
or log%285%2Cx%29=1
or x+=+5%5E1 [since for a>0 log%28a%2CM%29+=+b means M+=+a%5Eb]
or x=5

So the reqd. value of 'x' is 5.

Answer by Nate(3500) About Me  (Show Source):