Basic Math Examples

$\ln (18) \div \ln (6)$

Step 1

Rewrite the division as a fraction.

$\frac{\ln (18)}{\ln (6)}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $\ln (18)$ as $\ln (2 \cdot 3^{2})$ .

$\frac{\ln (2 \cdot 3^{2})}{\ln (6)}$

Step 2.2

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

$\frac{\ln (2) + \ln (3^{2})}{\ln (6)}$

Step 2.3

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

$\frac{\ln (2) + 2 \ln (3)}{\ln (6)}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $\ln (6)$ as $\ln (2 (3))$ .

$\frac{\ln (2) + 2 \ln (3)}{\ln (2 (3))}$

Step 3.2

Rewrite $\ln (2 (3))$ as $\ln (2) + \ln (3)$ .

$\frac{\ln (2) + 2 \ln (3)}{\ln (2) + \ln (3)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (2) + 2 \ln (3)}{\ln (2) + \ln (3)}$

Decimal Form:

$1.61314719 \dots$