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Write the expression 2 in3 + in8 as a single natural logarithm.

1 Answer

8 votes

Answer:


2\ln 3+\ln 8=\ln 72

Explanation:

Logarithms

Some properties of the logarithms are:


\ln xy = \ln x+\ln y


\ln x^n=n\ln x

We have:


2\ln 3+\ln 8

Applying the exponent property:


2\ln 3+\ln 8=\ln 3^2+\ln 8=\ln 9+\ln 8

Applying the product property:


2\ln 3+\ln 8=\ln (9*8)=\ln 72


\boxed{2\ln 3+\ln 8=\ln 72}

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