Question

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

Answer 1

`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}`