If 60^a=3 and 60^b=5, then 12^(1-a-b)/(2(1-b)) is

1983 AMC 12 Problem 25

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25.

60^a=3

and

60^b=5,

then

12^{\frac{1-a-b}{2(1-b)}}

\sqrt3

2

\sqrt5

3

\sqrt{12}

Express

1-a-b

and

1-b

as base-

60

logarithms

Use

1-a-b=\log_{60}4

and

1-b=\log_{60}12

Since

a=\log_{60}3

and

b=\log_{60}5,

\begin{aligned} 1-a-b &=\log_{60}\frac{60}{15}=\log_{60}4,\\ 1-b &=\log_{60}\frac{60}{5}=\log_{60}12. \end{aligned}

Therefore the exponent is

\frac12\log_{12}4,

and

12^{(\frac{1}{2})\log_{12}4}=\sqrt4=2.

Therefore, the correct answer is B.