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If log _{ 16 }{ 49 } =a and log _{ 7 }{ 25 } =b
then { 4 }^{ ab+1 } = ?

 May 23, 2022
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\(a = \log_{16} 49 = \dfrac12 \log_4 49 =\log_4 7\)

 

\(ab = \log_47 \cdot \log_725 = \dfrac{\ln 7}{\ln 4}\cdot \dfrac{\ln25}{\ln7} = \dfrac{\ln25}{\ln4} = \log_4 25\)

 

\(ab + 1 = \log_4 25 + 1 = \log_425 + \log_44 = \log_4100\)

 

That means \(4^{ab + 1} = 4^{\log_4 100} = 100\)

 May 23, 2022

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