If 10^log_109=8x+5, then x equals:

1965 AMC 12 Problem 6

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10^{\log_{10}9}=8x+5,

then

x

equals:

0

\dfrac12

\dfrac58

\dfrac98

\dfrac{2\log_{10}3-5}{8}

Use

10^{\log_{10}9}=9

Solve the resulting linear equation

9=8x+5

The exponential and logarithm cancel, so

10^{\log_{10}9}=9.

Thus

8x+5=9,

giving

x=\frac{1}{2}.

Therefore, the correct answer is B.