Precalculus Examples

$\log_{8} (11 x^{8}) + \log_{8} (6 x^{7})$

Step 1

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

$\log_{8} (11 x^{8} (6 x^{7}))$

Step 2

Rewrite using the commutative property of multiplication.

$\log_{8} (11 \cdot 6 x^{8} x^{7})$

Step 3

Multiply $x^{8}$ by $x^{7}$ by adding the exponents.

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Step 3.1

Move $x^{7}$ .

$\log_{8} (11 \cdot 6 (x^{7} x^{8}))$

Step 3.2

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

$\log_{8} (11 \cdot 6 x^{7 + 8})$

Step 3.3

Add $7$ and $8$ .

$\log_{8} (11 \cdot 6 x^{15})$

Step 4

Multiply $11$ by $6$ .

$\log_{8} (66 x^{15})$