SOLUTION: Could you please provide me with a detailed explantation on how to solve the following... log 2 {{{ (8^x) }}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Could you please provide me with a detailed explantation on how to solve the following... log 2 {{{ (8^x) }}}       Log On


   

Question 193540: Could you please provide me with a detailed explantation on how to solve the following...
log 2 +%288%5Ex%29+

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You can't solve this (ie you can't find "x"), but you can simplify


log%282%2C%288%5Ex%29%29 Start with the given expression.


x%2Alog%282%2C%288%29%29 Pull down the exponent using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29.


x%2Alog%282%2C%282%5E3%29%29 Rewrite 8 as 2%5E3


3x%2Alog%282%2C%282%29%29 Pull down the exponent using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29.


3x%2A%281%29 Evaluate the log base 2 of 2 to get 1


3x Multiply


So log%282%2C%288%5Ex%29%29=3x