SOLUTION: which logarithmic equation is equivalent to the exponential equation below? 8^x=100 a. x=log8 100 b. x=log100 8 c. 100=logx 8 b. 8=logx 100

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: which logarithmic equation is equivalent to the exponential equation below? 8^x=100 a. x=log8 100 b. x=log100 8 c. 100=logx 8 b. 8=logx 100      Log On


   

Question 145339: which logarithmic equation is equivalent to the exponential equation below?
8^x=100
a. x=log8 100
b. x=log100 8
c. 100=logx 8
b. 8=logx 100
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
8%5Ex=100+ Start with the given equation.


log%2810%2C%288%5Ex%29%29=log%2810%2C%28100%29%29+ Take the log base 10 of both sides.


x%2Alog%2810%2C%288%29%29=log%2810%2C%28100%29%29+ Rewrite the left side using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29.


x=log%2810%2C%28100%29%29%2Flog%2810%2C%288%29%29+ Divide both sides by log%2810%2C%288%29%29 to isolate x.


x=log%288%2C%28100%29%29 Use the change of base formula to simplify.


So 8%5Ex=100+ is equivalent to x=log%288%2C%28100%29%29