Precalculus Examples

$5 \log_{3} (x) + \log_{3} (x - 6)$

Step 1

Simplify $5 \log_{3} (x)$ by moving $5$ inside the logarithm.

$\log_{3} (x^{5}) + \log_{3} (x - 6)$

Step 2

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

$\log_{3} (x^{5} (x - 6))$

Step 3

Apply the distributive property.

$\log_{3} (x^{5} x + x^{5} \cdot - 6)$

Step 4

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

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Step 4.1

Multiply $x^{5}$ by $x$ .

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Step 4.1.1

Raise $x$ to the power of $1$ .

$\log_{3} (x^{5} x^{1} + x^{5} \cdot - 6)$

Step 4.1.2

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

$\log_{3} (x^{5 + 1} + x^{5} \cdot - 6)$

Step 4.2

Add $5$ and $1$ .

$\log_{3} (x^{6} + x^{5} \cdot - 6)$

Step 5

Move $- 6$ to the left of $x^{5}$ .

$\log_{3} (x^{6} - 6 x^{5})$