Question

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

Answer 1

Answer:

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

Step-by-step 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:

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

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