## zmudz one year ago If $$60^a = 3$$ and $$60^b = 5$$, then find $$12^{\frac{1-a-b}{2(1-b)}}.$$

1. freckles

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

2. freckles

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

3. freckles

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

4. ganeshie8

$$60^a = 3$$ and $$60^b = 5$$ multiplying gives $$60^{a+b} = 15 \implies 60^{1-a-b} =\frac{60}{15}=4$$ $$60^b = 5 \implies 60^{b-1} = \frac{5}{60} \implies 60^{1-b} = 12$$ $12^{\frac{1-a-b}{2(1-b)}}. = \left(60^{1-b}\right)^{\frac{1-a-b}{2(1-b)}} =\left( 60^{1-a-b}\right)^{1/2}=(4)^{1/2}=2$

5. freckles

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