Precalculus Examples

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

Step 1

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

$\ln (4 x (2 x))$

Step 2

Rewrite using the commutative property of multiplication.

$\ln (4 \cdot 2 x \cdot x)$

Step 3

Multiply $x$ by $x$ by adding the exponents.

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Step 3.1

Move $x$ .

$\ln (4 \cdot 2 (x \cdot x))$

Step 3.2

Multiply $x$ by $x$ .

$\ln (4 \cdot 2 x^{2})$

Step 4

Multiply $4$ by $2$ .

$\ln (8 x^{2})$