Precalculus Examples

$\log (7 \sqrt{x} - \log (7 x^{6}))$

Step 1

Rewrite $\log (7 x^{6})$ as $\log (7) + \log (x^{6})$ .

$\log (7 \sqrt{x} - (\log (7) + \log (x^{6})))$

Step 2

Expand $\log (x^{6})$ by moving $6$ outside the logarithm.

$\log (7 \sqrt{x} - (\log (7) + 6 \log (x)))$

Step 3

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

$\log (7 x^{\frac{1}{2}} - (\log (7) + 6 \log (x)))$

Step 4

Apply the distributive property.

$\log (7 x^{\frac{1}{2}} - \log (7) - (6 \log (x)))$

Step 5

Multiply $6$ by $- 1$ .

$\log (7 x^{\frac{1}{2}} - \log (7) - 6 \log (x))$