Precalculus Examples

$\frac{\frac{\ln (\frac{1}{2})}{22}}{88}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{\ln (\frac{1}{2})}{22} \cdot \frac{1}{88}$

Step 2

Rewrite $\frac{\ln (\frac{1}{2})}{22}$ as $\frac{1}{22} \ln (\frac{1}{2})$ .

$\frac{1}{22} \ln (\frac{1}{2}) \frac{1}{88}$

Step 3

Simplify $\frac{1}{22} \ln (\frac{1}{2})$ by moving $\frac{1}{22}$ inside the logarithm.

$\ln ({(\frac{1}{2})}^{\frac{1}{22}}) \frac{1}{88}$

Step 4

Apply the product rule to $\frac{1}{2}$ .

$\ln (\frac{1^{\frac{1}{22}}}{2^{\frac{1}{22}}}) \frac{1}{88}$

Step 5

One to any power is one.

$\ln (\frac{1}{2^{\frac{1}{22}}}) \frac{1}{88}$

Step 6

Multiply $\ln (\frac{1}{2^{\frac{1}{22}}}) \frac{1}{88}$ .

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Step 6.1

Reorder $\ln (\frac{1}{2^{\frac{1}{22}}})$ and $\frac{1}{88}$ .

$\frac{1}{88} \ln (\frac{1}{2^{\frac{1}{22}}})$

Step 6.2

Simplify $\frac{1}{88} \ln (\frac{1}{2^{\frac{1}{22}}})$ by moving $\frac{1}{88}$ inside the logarithm.

$\ln ({(\frac{1}{2^{\frac{1}{22}}})}^{\frac{1}{88}})$

Step 7

Apply the product rule to $\frac{1}{2^{\frac{1}{22}}}$ .

$\ln (\frac{1^{\frac{1}{88}}}{{(2^{\frac{1}{22}})}^{\frac{1}{88}}})$

Step 8

One to any power is one.

$\ln (\frac{1}{{(2^{\frac{1}{22}})}^{\frac{1}{88}}})$

Step 9

Multiply the exponents in ${(2^{\frac{1}{22}})}^{\frac{1}{88}}$ .

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Step 9.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\ln (\frac{1}{2^{\frac{1}{22} \cdot \frac{1}{88}}})$

Step 9.2

Multiply $\frac{1}{22} \cdot \frac{1}{88}$ .

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Step 9.2.1

Multiply $\frac{1}{22}$ by $\frac{1}{88}$ .

$\ln (\frac{1}{2^{\frac{1}{22 \cdot 88}}})$

Step 9.2.2

Multiply $22$ by $88$ .

$\ln (\frac{1}{2^{\frac{1}{1936}}})$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\ln (\frac{1}{2^{\frac{1}{1936}}})$

Decimal Form:

$- 0.00035803 \dots$