Precalculus Examples

$e \ln (8 x^{4})$

Step 1

Rewrite $\ln (8 x^{4})$ as $\ln (8) + \ln (x^{4})$ .

$e (\ln (8) + \ln (x^{4}))$

Step 2

Expand $\ln (x^{4})$ by moving $4$ outside the logarithm.

$e (\ln (8) + 4 \ln (x))$

Step 3

Simplify each term.

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Step 3.1

Rewrite $\ln (8)$ as $\ln (2^{3})$ .

$e (\ln (2^{3}) + 4 \ln (x))$

Step 3.2

Expand $\ln (2^{3})$ by moving $3$ outside the logarithm.

$e (3 \ln (2) + 4 \ln (x))$

Step 4

Apply the distributive property.

$e (3 \ln (2)) + e (4 \ln (x))$

Step 5

Simplify each term.

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Step 5.1

Move $3$ to the left of $e$ .

$3 \cdot e \ln (2) + e \cdot 4 \ln (x)$

Step 5.2

Move $4$ to the left of $e$ .

$3 e \ln (2) + 4 e \ln (x)$