Precalculus Examples

$\log_{m} (30 x^{2})$

Step 1

Rewrite $\log_{m} (30 x^{2})$ as $\log_{m} (30) + \log_{m} (x^{2})$ .

$\log_{m} (30) + \log_{m} (x^{2})$

Step 2

Expand $\log_{m} (x^{2})$ by moving $2$ outside the logarithm.

$\log_{m} (30) + 2 \log_{m} (x)$

Step 3

Simplify each term.

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Step 3.1

Rewrite $\log_{m} (30)$ as $\log_{m} (2 \cdot 3 \cdot 5)$ .

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

Step 3.2

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

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

Step 3.3

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

$\log_{m} (2) + \log_{m} (3) + \log_{m} (5) + 2 \log_{m} (x)$