Question

Use properties of logarithms to write each expression below as a single logarithm.

Answer 1

ln(12x⁵)

Explanation:

Given the logarithmic expression:

`\ln (4x^2)+\ln (3x^3)`

Apply the log rule below:

`\log _ca+\log _cb=\log _c(ab)`

Therefore:

`\begin{gathered} \ln (4x^2)+\ln (3x^3)=\ln (4x^2*3x^3) \\ =\ln (4*3* x^2* x^3) \\ =\ln (12* x^(2+3)) \\ =\ln (12x^5) \end{gathered}`

The logarithm expressed as a single logarithm is ln(12x⁵).