SOLUTION: Solve using logarithms. Round any decimal answers to the nearest hundredth. Do not use spaces or captial letters. (1/8)^x=606

Algebra ->  Algebra  -> Exponential-and-logarithmic-functions -> SOLUTION: Solve using logarithms. Round any decimal answers to the nearest hundredth. Do not use spaces or captial letters. (1/8)^x=606      Log On

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Question 78560: Solve using logarithms. Round any decimal answers to the nearest hundredth. Do not use spaces or captial letters.
(1/8)^x=606
Answer by tutor_paul(427) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F8%29%5Ex=606
Take the log of both sides of the equation:
log%28%281%2F8%29%5Ex%29=log%28606%29
Use the exponent property of logarithms to simplify left side:
xlog%281%2F8%29=log%28606%29
Use the division property of logarthms to further simplify left hand side:
x%28log%281%29-log%288%29%29=log%28606%29
Recall that log(1)=0 and solve for x:
x=-%28log%28606%29%2Flog%288%29%29
I'll let you plug that into a calculator to get a numerical value for x.
Good Luck,
tutor_paul@yahoo.com