If 8^x=32, then x equals:

1962 AMC 12 Problem 4

Attempt Problem 4 of the 1962 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1962 AMC 12 solutions, or check the answer key.

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8^x=32,

then

x

equals:

4

\dfrac53

\dfrac32

\dfrac35

\dfrac14

Express both sides as powers of

2

Equate the exponents in

2^{3x}=2^5

Since

8=2^3

and

32=2^5,

the equation becomes

2^{3x}=2^5.

Hence

3x=5

and

x=\frac{5}{3}.

Therefore, the correct answer is B.