SOLUTION: What does x equal in the logarithm equation log<sub>8</sub>(4) = x·log<sub>8</sub>(2) ?

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Question 641759: What does x equal in the logarithm equation
log8(4) = x·log8(2) ?
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
log8(4) = x·log8(2)

Write the 4 as 2˛

log8(2˛) = x·log8(2)

Now use this rule of lagarithms: log%28B%2C%28A%5EC%29%29=C%2Alog%28B%2CA%29 on the left

2·log8(2) = x·log8(2)

Divide both sides by log8(2)

2%2Alog%288%2C%282%29%29%2Flog%288%2C%282%29%29 = x%2Alog%288%2C%282%29%29%2Flog%288%2C%282%29%29 

2%2Across%28log%288%2C%282%29%29%29%2Fcross%28log%288%2C%282%29%29%29 = x%2Across%28log%288%2C%282%29%29%29%2Fcross%28log%288%2C%282%29%29%29

 2 = x

Edwin