Precalculus Examples

$\ln (\frac{63 x^{2}}{5})$

Step 1

Rewrite $\ln (\frac{63 x^{2}}{5})$ as $\ln (63 x^{2}) - \ln (5)$ .

$\ln (63 x^{2}) - \ln (5)$

Step 2

Rewrite $\ln (63 x^{2})$ as $\ln (63) + \ln (x^{2})$ .

$\ln (63) + \ln (x^{2}) - \ln (5)$

Step 3

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

$\ln (63) + 2 \ln (x) - \ln (5)$

Step 4

Simplify each term.

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Step 4.1

Rewrite $\ln (63)$ as $\ln (3^{2} \cdot 7)$ .

$\ln (3^{2} \cdot 7) + 2 \ln (x) - \ln (5)$

Step 4.2

Rewrite $\ln (3^{2} \cdot 7)$ as $\ln (3^{2}) + \ln (7)$ .

$\ln (3^{2}) + \ln (7) + 2 \ln (x) - \ln (5)$

Step 4.3

Expand $\ln (3^{2})$ by moving $2$ outside the logarithm.

$2 \ln (3) + \ln (7) + 2 \ln (x) - \ln (5)$