Precalculus Examples

$8 \log_{2} (\sqrt{3 x - 2} - \log_{2} (\frac{4}{x}) + \log_{2} (4))$

Step 1

Rewrite $\log_{2} (\frac{4}{x})$ as $\log_{2} (4) - \log_{2} (x)$ .

$8 \log_{2} (\sqrt{3 x - 2} - (\log_{2} (4) - \log_{2} (x)) + \log_{2} (4))$

Step 2

Logarithm base $2$ of $4$ is $2$ .

$8 \log_{2} (\sqrt{3 x - 2} - (2 - \log_{2} (x)) + \log_{2} (4))$

Step 3

Logarithm base $2$ of $4$ is $2$ .

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

Step 4

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

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

Step 5

Apply the distributive property.

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

Step 6

Multiply $- 1$ by $2$ .

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

Step 7

Multiply $- - \log_{2} (x)$ .

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Step 7.1

Multiply $- 1$ by $- 1$ .

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

Step 7.2

Multiply $\log_{2} (x)$ by $1$ .

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

Step 8

Add $- 2$ and $2$ .

$8 \log_{2} ({(3 x - 2)}^{\frac{1}{2}} + 0 + \log_{2} (x))$

Step 9

Add ${(3 x - 2)}^{\frac{1}{2}}$ and $0$ .

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