Precalculus Examples

$\log_{3} (\frac{1}{27}) + \log_{2} ({(\frac{1}{4})}^{2})$

Step 1

Simplify each term.

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Step 1.1

Logarithm base $3$ of $\frac{1}{27}$ is $- 3$ .

$- 3 + \log_{2} ({(\frac{1}{4})}^{2})$

Step 1.2

Apply the product rule to $\frac{1}{4}$ .

$- 3 + \log_{2} (\frac{1^{2}}{4^{2}})$

Step 1.3

One to any power is one.

$- 3 + \log_{2} (\frac{1}{4^{2}})$

Step 1.4

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

$- 3 + \log_{2} (\frac{1}{16})$

Step 1.5

Logarithm base $2$ of $\frac{1}{16}$ is $- 4$ .

$- 3 - 4$

Step 2

Subtract $4$ from $- 3$ .

$- 7$