If P=(s)/((1+k)^n), then n equals:

1958 AMC 12 Problem 12

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12.

P=\dfrac{s}{(1+k)^n},

then

n

equals:

\dfrac{\log(\frac{s}{P})}{\log(1+k)}

\log\dfrac{s}{P(1+k)}

\log\dfrac{s-P}{1+k}

\log\dfrac{s}{P}+\log(1+k)

\dfrac{\log s}{\log(P(1+k))}

Take logarithms of both sides of the equation

Use

\log P=\log s-n\log(1+k)

and isolate

n

Taking logarithms,

\log P=\log s-n\log(1+k).

Therefore

n=\frac{\log s-\log P}{\log(1+k)} =\frac{\log(\frac{s}{P})}{\log(1+k)}.

Thus, the correct answer is A.