Finite Math Examples

$\log_{5} (1250) - \log_{5} (2)$

Step 1

Simplify each term.

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Step 1.1

Rewrite $\log_{5} (1250)$ as $\log_{5} (2 \cdot 5^{4})$ .

$\log_{5} (2 \cdot 5^{4}) - \log_{5} (2)$

Step 1.2

Rewrite $\log_{5} (2 \cdot 5^{4})$ as $\log_{5} (2) + \log_{5} (5^{4})$ .

$\log_{5} (2) + \log_{5} (5^{4}) - \log_{5} (2)$

Step 1.3

Use logarithm rules to move $4$ out of the exponent.

$\log_{5} (2) + 4 \log_{5} (5) - \log_{5} (2)$

Step 1.4

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

$\log_{5} (2) + 4 \cdot 1 - \log_{5} (2)$

Step 1.5

Multiply $4$ by $1$ .

$\log_{5} (2) + 4 - \log_{5} (2)$

Step 2

Subtract $\log_{5} (2)$ from $\log_{5} (2)$ .

$0 + 4$

Step 3

Add $0$ and $4$ .

$4$