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zmudz

  • one year ago

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

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

  2. freckles
    • one year ago
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    we could just solve for a and b directly and in plug in but what would be the fun in that

  3. freckles
    • one year ago
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    that might have to be what you do just solve both of the equations for a and b then plugin'

  4. ganeshie8
    • one year ago
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    \(60^a = 3\) 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
    • one year ago
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    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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