Precalculus Examples

$2 \log_{5} (\sqrt{3 x - 8})$

Step 1

Simplify $2 \log_{5} (\sqrt{3 x - 8})$ by moving $2$ inside the logarithm.

$\log_{5} ({\sqrt{3 x - 8}}^{2})$

Step 2

Rewrite ${\sqrt{3 x - 8}}^{2}$ as $3 x - 8$ .

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x - 8}$ as ${(3 x - 8)}^{\frac{1}{2}}$ .

$\log_{5} ({({(3 x - 8)}^{\frac{1}{2}})}^{2})$

Step 2.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\log_{5} ({(3 x - 8)}^{\frac{1}{2} \cdot 2})$

Step 2.3

Combine $\frac{1}{2}$ and $2$ .

$\log_{5} ({(3 x - 8)}^{\frac{2}{2}})$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

$\log_{5} ({(3 x - 8)}^{\frac{2}{2}})$

Step 2.4.2

Rewrite the expression.

$\log_{5} ({(3 x - 8)}^{1})$

Step 2.5

Simplify.

$\log_{5} (3 x - 8)$