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Algebra
Pregunta

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

10

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

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

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

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

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

Solución
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