Suppose that $\ln A = 3$ and $\ln B = 4$ . Fin...

Question

$Suppose that $\ln A = 3$ and $\ln B = 4$ . Fin...$

Suppose that $\ln A = 3$ and $\ln B = 4$ . Find the exact value of $\ln ( A ^ { 2 } \cdot B )$ .

Answer

$\ln ( A ^ { 2 } B ) = 2 \ln ( A ) + \ln ( B )$

$\ln ( A ^ { 2 } B )$

Apply log rule: $ \log _ { c } ( a b ) = \log _ { c } ( a ) + \log _ { c } ( b )$

$\ln ( A ^ { 2 } B ) = \ln ( A ^ { 2 } ) + \ln ( B )$

$= \ln ( A ^ { 2 } ) + \ln ( B )$

Apply log rule: $ \log _ { a } ( x ^ { b } ) = b - \log _ { a } ( x )$

$\ln ( A ^ { 2 } ) = 2 \ln ( A )$

$= 2 \ln ( A ) + \ln ( B )$

Solution

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