Precalculus Examples

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

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1

Apply the product rule to $7 x y$ .

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

Step 1.2

Apply the product rule to $7 x$ .

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

Step 2

Raise $7$ to the power of $3$ .

$\log_{3} (343 x^{3} y^{3})$

Step 3

Rewrite $\log_{3} (343 x^{3} y^{3})$ using the change of base formula.

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Step 3.1

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 3.2

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

$\frac{\log (343 x^{3} y^{3})}{\log (3)}$