Precalculus Examples

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

Step 1

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

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

Step 2

Apply the distributive property.

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

Step 3

Simplify the expression.

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Step 3.1

Rewrite using the commutative property of multiplication.

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

Step 3.2

Multiply $3$ by $2$ .

$\ln (3 x \cdot x + 6 x)$

Step 4

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

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Step 4.1

Move $x$ .

$\ln (3 (x \cdot x) + 6 x)$

Step 4.2

Multiply $x$ by $x$ .

$\ln (3 x^{2} + 6 x)$