Question

write the following expression as a sum and/or difference of logarithms. express powers as factors. \\(\ln e(x + 9)\\) \\(\ln e(x + 9) = \square\\) (simplify your answer.)

Explanation:

Step1: Apply logarithm product rule

The logarithm of a product is the sum of the logarithms, so $\ln[ e(x + 9) ]=\ln(e)+\ln(x + 9)$.

Step2: Simplify $\ln(e)$

We know that $\ln(e) = 1$ (since the natural logarithm of the base $e$ is 1). So substituting this in, we get $1+\ln(x + 9)$.

Answer:

$1 + \ln(x + 9)$