Question

If \(60^a = 3\) and \(60^b = 5\), then find \(12^{\frac{1-a-b}{2(1-b)}}.\)

Answer 1

\[60=5(12) \\ 60^a=5^a (12)^a=3 \\ 12^a=\frac{3}{5^a} \\ 5^b 12^b=5 \\ 12^b=\frac{5}{5^b}=5^{1-b}\]
maybe you can somehow use this

Answer 2

we could just solve for a and b directly and in plug in but what would be the fun in that

Answer 3

that might have to be what you do
just solve both of the equations for a and b
then plugin'

Answer 4

\(60^a = 3\) and \(60^b = 5\)
multiplying gives \(60^{a+b} = 15 \implies 60^{1-a-b} =\frac{60}{15}=4\)

\(60^b = 5 \implies 60^{b-1} = \frac{5}{60} \implies 60^{1-b} = 12\)

\[12^{\frac{1-a-b}{2(1-b)}}. = \left(60^{1-b}\right)^{\frac{1-a-b}{2(1-b)}} =\left( 60^{1-a-b}\right)^{1/2}=(4)^{1/2}=2\]

Answer 5

much better than what I did
found 2 the long way around
or one of the longer ways if there is another