1968 AMC 12 Problem 2

Attempt Problem 2 of the 1968 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 1968 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

The real value of

x

such that

64^{x-1}

divided by

4^{x-1}

equals

256^{2x}

is:

-\dfrac23

-\dfrac13

0

\dfrac14

\dfrac38

Combine the quotient because its powers have the same exponent

Write both sides as powers of

16

The left side is

(\frac{64}{4})^{x-1}=16^{x-1},

while

256^{2x}=(16^2)^{2x}=16^{4x}.

Hence

x-1=4x,

x=-\frac{1}{3}.

Therefore, the correct answer is B.

Problem 2 in other years