Precalculus Examples

$\log_{2} (40) - \log_{2} (5)$

Step 1

Simplify each term.

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Step 1.1

Rewrite $\log_{2} (40)$ as $\log_{2} (2^{3} \cdot 5)$ .

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

Step 1.2

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

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

Step 1.3

Use logarithm rules to move $3$ out of the exponent.

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

Step 1.4

Logarithm base $2$ of $2$ is $1$ .

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

Step 1.5

Multiply $3$ by $1$ .

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

Step 2

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

$3 + 0$

Step 3

Add $3$ and $0$ .

$3$