Use the laws of logarithms to write the expression as the logarithm of a single quantity. 4 ln 5 - $\frac{5}{6}$ ln (x + 6)
A) $\frac{5 \ln 625}{6(x+6)}$
B) $\ln 5^{4}-\ln (x+6)^{5 / 6}$
C) $\frac{4 \ln 5}{\frac{5}{6} \ln (x+6)}$
D) $\ln \frac{625}{(x+6)^{5 / 6}}$

Question

Quizplus · Accepted Answer

We can use the laws of logarithms to combine the terms as follows:

4 ln 5 - $\frac{5}{6}$ ln (x + 6) = ln 5^4 - ln (x + 6)^{5/6}

Then, we can use the quotient rule of logarithms to simplify further:

ln 5^4 - ln (x + 6)^{5/6} = ln$\frac{5^4}{(x+6)^{5/6}}$

This gives us answer choice D.

Use the Laws of Logarithms to Write the Expression as the Logarithm