Problem

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) $\ln e^{5}-\ln e^{2}=\square$.

Solution

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: \(\boxed{2}\)

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