Precalculus Examples

$\frac{1}{0.03} \cdot \ln (\frac{78}{78 - 54})$

Step 1

Divide $1$ by $0.03$ .

$33.\overline{3} \cdot \ln (\frac{78}{78 - 54})$

Step 2

Cancel the common factor of $78$ and $78 - 54$ .

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Step 2.1

Factor $6$ out of $78$ .

$33.\overline{3} \cdot \ln (\frac{6 (13)}{78 - 54})$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $6$ out of $78$ .

$33.\overline{3} \cdot \ln (\frac{6 \cdot 13}{6 \cdot 13 - 54})$

Step 2.2.2

Factor $6$ out of $- 54$ .

$33.\overline{3} \cdot \ln (\frac{6 (13)}{6 \cdot 13 + 6 \cdot - 9})$

Step 2.2.3

Factor $6$ out of $6 \cdot 13 + 6 \cdot - 9$ .

$33.\overline{3} \cdot \ln (\frac{6 (13)}{6 \cdot (13 - 9)})$

Step 2.2.4

Cancel the common factor.

$33.\overline{3} \cdot \ln (\frac{6 \cdot 13}{6 \cdot (13 - 9)})$

Step 2.2.5

Rewrite the expression.

$33.\overline{3} \cdot \ln (\frac{13}{13 - 9})$

Step 3

Subtract $9$ from $13$ .

$33.\overline{3} \cdot \ln (\frac{13}{4})$

Step 4

Simplify $33.\overline{3} \ln (\frac{13}{4})$ by moving $33.\overline{3}$ inside the logarithm.

$\ln ({(\frac{13}{4})}^{33.\overline{3}})$

Step 5

Apply the product rule to $\frac{13}{4}$ .

$\ln (\frac{13^{33.\overline{3}}}{4^{33.\overline{3}}})$

Step 6

Raise $4$ to the power of $33.\overline{3}$ .

$\ln (\frac{13^{33.\overline{3}}}{117129523791979000000})$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\ln (\frac{13^{33.\overline{3}}}{117129523791979000000})$

Decimal Form:

$39.28849987 \dots$