Precalculus Examples

$\log_{729} (\frac{1}{27})$

Step 1

Rewrite $\log_{729} (\frac{1}{27})$ as $\log_{729} (1) - \log_{729} (27)$ .

$\log_{729} (1) - \log_{729} (27)$

Step 2

Logarithm base $729$ of $1$ is $0$ .

$0 - \log_{729} (27)$

Step 3

Logarithm base $729$ of $27$ is $\frac{1}{2}$ .

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Step 3.1

Factor $3$ out of $3$ .

$0 - \frac{3 (1)}{6}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $6$ .

$0 - \frac{3 \cdot 1}{3 \cdot 2}$

Step 3.2.2

Cancel the common factor.

$0 - \frac{3 \cdot 1}{3 \cdot 2}$

Step 3.2.3

Rewrite the expression.

$0 - \frac{1}{2}$

Step 4

Subtract $\frac{1}{2}$ from $0$ .

$- \frac{1}{2}$