Precalculus Examples

$\log_{5} (5^{75}) - \log_{5} (5^{2}) \cdot 3$

Step 1

Simplify each term.

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Step 1.1

Use logarithm rules to move $75$ out of the exponent.

$75 \log_{5} (5) - \log_{5} (5^{2}) \cdot 3$

Step 1.2

Logarithm base $5$ of $5$ is $1$ .

$75 \cdot 1 - \log_{5} (5^{2}) \cdot 3$

Step 1.3

Multiply $75$ by $1$ .

$75 - \log_{5} (5^{2}) \cdot 3$

Step 1.4

Use logarithm rules to move $2$ out of the exponent.

$75 - (2 \log_{5} (5)) \cdot 3$

Step 1.5

Logarithm base $5$ of $5$ is $1$ .

$75 - (2 \cdot 1) \cdot 3$

Step 1.6

Multiply $2$ by $1$ .

$75 - 1 \cdot 2 \cdot 3$

Step 1.7

Multiply $- 1 \cdot 2 \cdot 3$ .

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Step 1.7.1

Multiply $- 1$ by $2$ .

$75 - 2 \cdot 3$

Step 1.7.2

Multiply $- 2$ by $3$ .

$75 - 6$

Step 2

Subtract $6$ from $75$ .

$69$