Trigonometry Examples

$\log_{5} (510)$

Step 1

Rewrite $\log_{5} (510)$ as $\log_{5} (2 \cdot 3 \cdot 5 \cdot 17)$ .

$\log_{5} (2 \cdot 3 \cdot 5 \cdot 17)$

Step 2

Rewrite $\log_{5} (2 \cdot 3 \cdot 5 \cdot 17)$ as $\log_{5} (2 \cdot 3 \cdot 5) + \log_{5} (17)$ .

$\log_{5} (2 \cdot 3 \cdot 5) + \log_{5} (17)$

Step 3

Simplify each term.

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Step 3.1

Rewrite $\log_{5} (2 \cdot 3 \cdot 5)$ as $\log_{5} (2 \cdot 3) + \log_{5} (5)$ .

$\log_{5} (2 \cdot 3) + \log_{5} (5) + \log_{5} (17)$

Step 3.2

Simplify each term.

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Step 3.2.1

Rewrite $\log_{5} (2 \cdot 3)$ as $\log_{5} (2) + \log_{5} (3)$ .

$\log_{5} (2) + \log_{5} (3) + \log_{5} (5) + \log_{5} (17)$

Step 3.2.2

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

$\log_{5} (2) + \log_{5} (3) + 1 + \log_{5} (17)$