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

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freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[60=5(12) \\ 60^a=5^a (12)^a=3 \\ 12^a=\frac{3}{5^a} \\ 5^b 12^b=5 \\ 12^b=\frac{5}{5^b}=5^{1b}\] maybe you can somehow use this

freckles
 one year ago
Best ResponseYou've already chosen the best response.1we could just solve for a and b directly and in plug in but what would be the fun in that

freckles
 one year ago
Best ResponseYou've already chosen the best response.1that might have to be what you do just solve both of the equations for a and b then plugin'

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2\(60^a = 3\) and \(60^b = 5\) multiplying gives \(60^{a+b} = 15 \implies 60^{1ab} =\frac{60}{15}=4\) \(60^b = 5 \implies 60^{b1} = \frac{5}{60} \implies 60^{1b} = 12\) \[12^{\frac{1ab}{2(1b)}}. = \left(60^{1b}\right)^{\frac{1ab}{2(1b)}} =\left( 60^{1ab}\right)^{1/2}=(4)^{1/2}=2\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1much 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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