Exponential and Logarithmic Functions
Using properties of logarithms to evaluate expressions

Use the properties of logarithms to evaluate each of the following expres
(a) $\log _{6} 4+2 \log _{6} 3=\square$
(b) $\ln e^{5}-\ln e^{2}=\square$.

Answer

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Answer

Final Answer: $\boxed{2}$

Steps

Step 1 ：First, we calculate the logarithm base 6 of 4, which is approximately 0.7737056144690831.

Step 2 ：Next, we calculate the logarithm base 6 of 3 squared, which is approximately 1.226294385530917.

Step 3 ：We then add the two results together, which gives us a final result of 2.0.

Step 4 ：Therefore, the expression $ \log _{6} 4+2 \log _{6} 3 $ simplifies to 2.

Step 5 ：Final Answer: $\boxed{2}$