Precalculus Examples

$\log (40) + 2 \cdot \log (5)$

Step 1

Simplify each term.

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Step 1.1

Simplify $2 \log (5)$ by moving $2$ inside the logarithm.

$\log (40) + \log (5^{2})$

Step 1.2

Raise $5$ to the power of $2$ .

$\log (40) + \log (25)$

Step 2

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log (40 \cdot 25)$

Step 3

Multiply $40$ by $25$ .

$\log (1000)$

Step 4

Logarithm base $10$ of $1000$ is $3$ .

$3$