Precalculus Examples

$\log_{7} (700)$

Step 1

Rewrite $\log_{7} (700)$ as $\log_{7} (2^{2} \cdot 5^{2} \cdot 7)$ .

$\log_{7} (2^{2} \cdot 5^{2} \cdot 7)$

Step 2

Rewrite $\log_{7} (2^{2} \cdot 5^{2} \cdot 7)$ as $\log_{7} (2^{2} \cdot 5^{2}) + \log_{7} (7)$ .

$\log_{7} (2^{2} \cdot 5^{2}) + \log_{7} (7)$

Step 3

Simplify each term.

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Step 3.1

Rewrite $\log_{7} (2^{2} \cdot 5^{2})$ as $\log_{7} (2^{2}) + \log_{7} (5^{2})$ .

$\log_{7} (2^{2}) + \log_{7} (5^{2}) + \log_{7} (7)$

Step 3.2

Simplify each term.

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Step 3.2.1

Expand $\log_{7} (2^{2})$ by moving $2$ outside the logarithm.

$2 \log_{7} (2) + \log_{7} (5^{2}) + \log_{7} (7)$

Step 3.2.2

Expand $\log_{7} (5^{2})$ by moving $2$ outside the logarithm.

$2 \log_{7} (2) + 2 \log_{7} (5) + \log_{7} (7)$

Step 3.3

Logarithm base $7$ of $7$ is $1$ .

$2 \log_{7} (2) + 2 \log_{7} (5) + 1$