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Algebra
Question

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

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

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

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

Solution
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