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Exponentiation Problem

Can anyone please help me in solving this problem?

\(60^{a} = 3\)

\(60^{b} = 5\)

\(12^{\frac{1 - a - b}{2(1 - b)}} = ?\)

I am just unable to solve it. So, any help would be highly appreciated.

Thanks.

Note by Nilabha Saha
5 months, 2 weeks ago

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\(a=\dfrac{\log3}{\log{60}}\). \(b=\dfrac{\log5}{\log{60}}\).

\(12^{\frac{1-(a+b)}{2(1-b)}}\)\(=12^{\frac{1-\log15/\log{60}}{2(1-\log5/{60})}}=\)\(12^{\frac{\log4/\log{60}}{2(\log{12}/\log{60})}}=\)\(12^{\log2/\log{12}}=12^{\log_{12}{2}}=2\).

Note:

\(\log a+\log b=\log{ab}\)

\(\log a-\log b=\log{a/b}\)

\(\log a^2=2 \log a\)

\(a^{\log_a b}=b\).

Here, we take \(1=\log{60}/\log{60}\). Svatejas Shivakumar · 5 months, 2 weeks ago

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@Svatejas Shivakumar Thank you very much.☺ Helped me understand a lot.😃😃😃 Nilabha Saha · 5 months, 2 weeks ago

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