Precalculus Examples

$\log (5) (3 x + 2)$

Step 1

Apply the distributive property.

$\log (5) (3 x) + \log (5) \cdot 2$

Step 2

Simplify $3 \log (5)$ by moving $3$ inside the logarithm.

$\log (5^{3}) x + \log (5) \cdot 2$

Step 3

Multiply $\log (5) \cdot 2$ .

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Step 3.1

Reorder $\log (5)$ and $2$ .

$\log (5^{3}) x + 2 \cdot \log (5)$

Step 3.2

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

$\log (5^{3}) x + \log (5^{2})$

Step 4

Simplify each term.

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Step 4.1

Raise $5$ to the power of $3$ .

$\log (125) x + \log (5^{2})$

Step 4.2

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

$\log (125) x + \log (25)$

Step 5

Reorder factors in $\log (125) x + \log (25)$ .

$x \log (125) + \log (25)$