Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

Simplify $8 \log (2)$ by moving $8$ inside the logarithm.

$\log (2^{8}) \sqrt{3 x - 2} - \log (2) \frac{4}{x}$

Step 1.2

Raise $2$ to the power of $8$ .

$\log (256) \sqrt{3 x - 2} - \log (2) \frac{4}{x}$

Step 1.3

Multiply $- \log (2) \frac{4}{x}$ .

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Step 1.3.1

Combine $\frac{4}{x}$ and $\log (2)$ .

$\log (256) \sqrt{3 x - 2} - \frac{4 \log (2)}{x}$

Step 1.3.2

Simplify $4 \log (2)$ by moving $4$ inside the logarithm.

$\log (256) \sqrt{3 x - 2} - \frac{\log (2^{4})}{x}$

Step 1.4

Raise $2$ to the power of $4$ .

$\log (256) \sqrt{3 x - 2} - \frac{\log (16)}{x}$

Step 2

To write $\log (256) \sqrt{3 x - 2}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{\log (256) \sqrt{3 x - 2} x}{x} - \frac{\log (16)}{x}$

Step 3

Combine the numerators over the common denominator.

$\frac{\log (256) \sqrt{3 x - 2} x - \log (16)}{x}$