zmudz
  • zmudz
If \(60^a = 3\) and \(60^b = 5\), then find \(12^{\frac{1-a-b}{2(1-b)}}.\)
Mathematics
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SOLVED
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chestercat
  • chestercat
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freckles
  • 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
freckles
  • freckles
we could just solve for a and b directly and in plug in but what would be the fun in that
freckles
  • freckles
that might have to be what you do just solve both of the equations for a and b then plugin'

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ganeshie8
  • ganeshie8
\(60^a = 3\) and \(60^b = 5\) multiplying gives \(60^{a+b} = 15 \implies 60^{1-a-b} =\frac{60}{15}=4\) \(60^b = 5 \implies 60^{b-1} = \frac{5}{60} \implies 60^{1-b} = 12\) \[12^{\frac{1-a-b}{2(1-b)}}. = \left(60^{1-b}\right)^{\frac{1-a-b}{2(1-b)}} =\left( 60^{1-a-b}\right)^{1/2}=(4)^{1/2}=2\]
freckles
  • freckles
much better than what I did found 2 the long way around or one of the longer ways if there is another

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