Precalculus Examples

$\frac{(21) \ln (\frac{111}{3})}{\ln (2)}$

Step 1

Cancel the common factor of $111$ and $3$ .

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Step 1.1

Factor $3$ out of $111$ .

$\frac{21 \ln (\frac{3 \cdot 37}{3})}{\ln (2)}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $3$ .

$\frac{21 \ln (\frac{3 \cdot 37}{3 (1)})}{\ln (2)}$

Step 1.2.2

Cancel the common factor.

$\frac{21 \ln (\frac{3 \cdot 37}{3 \cdot 1})}{\ln (2)}$

Step 1.2.3

Rewrite the expression.

$\frac{21 \ln (\frac{37}{1})}{\ln (2)}$

Step 1.2.4

Divide $37$ by $1$ .

$\frac{21 \ln (37)}{\ln (2)}$

Step 2

Simplify $21 \ln (37)$ by moving $21$ inside the logarithm.

$\frac{\ln (37^{21})}{\ln (2)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (37^{21})}{\ln (2)}$

Decimal Form:

$109.39852067 \dots$