Precalculus Examples

$3 \log_{3} (3) - \frac{3}{4} \cdot \log_{3} (81) + \frac{1}{3} \cdot \log_{3} (\frac{1}{27})$

Step 1

Simplify each term.

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Step 1.1

Logarithm base $3$ of $3$ is $1$ .

$3 \cdot 1 - \frac{3}{4} \cdot \log_{3} (81) + \frac{1}{3} \cdot \log_{3} (\frac{1}{27})$

Step 1.2

Multiply $3$ by $1$ .

$3 - \frac{3}{4} \cdot \log_{3} (81) + \frac{1}{3} \cdot \log_{3} (\frac{1}{27})$

Step 1.3

Logarithm base $3$ of $81$ is $4$ .

$3 - \frac{3}{4} \cdot 4 + \frac{1}{3} \cdot \log_{3} (\frac{1}{27})$

Step 1.4

Cancel the common factor of $4$ .

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Step 1.4.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$3 + \frac{- 3}{4} \cdot 4 + \frac{1}{3} \cdot \log_{3} (\frac{1}{27})$

Step 1.4.2

Cancel the common factor.

$3 + \frac{- 3}{4} \cdot 4 + \frac{1}{3} \cdot \log_{3} (\frac{1}{27})$

Step 1.4.3

Rewrite the expression.

$3 - 3 + \frac{1}{3} \cdot \log_{3} (\frac{1}{27})$

Step 1.5

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

$3 - 3 + \frac{1}{3} \cdot - 3$

Step 1.6

Cancel the common factor of $3$ .

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Step 1.6.1

Factor $3$ out of $- 3$ .

$3 - 3 + \frac{1}{3} \cdot (3 (- 1))$

Step 1.6.2

Cancel the common factor.

$3 - 3 + \frac{1}{3} \cdot (3 \cdot - 1)$

Step 1.6.3

Rewrite the expression.

$3 - 3 - 1$

Step 2

Simplify by subtracting numbers.

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Step 2.1

Subtract $3$ from $3$ .

$0 - 1$

Step 2.2

Subtract $1$ from $0$ .

$- 1$