Precalculus Examples

$\log (2 x^{4}) + \log (3 x^{5})$

Step 1

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

$\log (2 x^{4} (3 x^{5}))$

Step 2

Rewrite using the commutative property of multiplication.

$\log (2 \cdot 3 x^{4} x^{5})$

Step 3

Multiply $x^{4}$ by $x^{5}$ by adding the exponents.

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Step 3.1

Move $x^{5}$ .

$\log (2 \cdot 3 (x^{5} x^{4}))$

Step 3.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\log (2 \cdot 3 x^{5 + 4})$

Step 3.3

Add $5$ and $4$ .

$\log (2 \cdot 3 x^{9})$

Step 4

Multiply $2$ by $3$ .

$\log (6 x^{9})$