Precalculus Examples

$\log_{7} (\sqrt{x}) - \log_{7} ({(x)}^{3})$

Step 1

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{7} (\frac{\sqrt{x}}{x^{3}})$

Step 2

Rewrite $\log_{7} (\frac{\sqrt{x}}{x^{3}})$ using the change of base formula.

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Step 2.1

The change of base rule can be used if $a$ and $b$ are greater than $0$ and not equal to $1$ , and $x$ is greater than $0$ .

$\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}$

Step 2.2

Substitute in values for the variables in the change of base formula, using $b = 10$ .

$\frac{\log (\frac{\sqrt{x}}{x^{3}})}{\log (7)}$