Precalculus Examples

$\log_{5} (7 y^{5} x^{- 3})$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\log_{5} (7 y^{5} \frac{1}{x^{3}})$

Step 2

Multiply $7 y^{5} \frac{1}{x^{3}}$ .

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Step 2.1

Combine $7$ and $\frac{1}{x^{3}}$ .

$\log_{5} (y^{5} \frac{7}{x^{3}})$

Step 2.2

Combine $y^{5}$ and $\frac{7}{x^{3}}$ .

$\log_{5} (\frac{y^{5} \cdot 7}{x^{3}})$

Step 3

Move $7$ to the left of $y^{5}$ .

$\log_{5} (\frac{7 y^{5}}{x^{3}})$

Step 4

Rewrite $\log_{5} (\frac{7 y^{5}}{x^{3}})$ using the change of base formula.

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Step 4.1

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 4.2

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

$\frac{\log (\frac{7 y^{5}}{x^{3}})}{\log (5)}$