Precalculus Examples

$\ln (e^{7} x + 9) + 4 \ln (e^{3} x + 1)$

Step 1

Simplify $4 \ln (e^{3} x + 1)$ by moving $4$ inside the logarithm.

$\ln (e^{7} x + 9) + \ln ({(e^{3} x + 1)}^{4})$

Step 2

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\ln ((e^{7} x + 9) {(e^{3} x + 1)}^{4})$

Step 3

Apply the distributive property.

$\ln (e^{7} x {(e^{3} x + 1)}^{4} + 9 {(e^{3} x + 1)}^{4})$