Precalculus Examples

$\frac{\frac{\ln (2)}{41}}{- 0.0559}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{\ln (2)}{41} \cdot \frac{1}{- 0.0559}$

Step 2

Rewrite $\frac{\ln (2)}{41}$ as $\frac{1}{41} \ln (2)$ .

$\frac{1}{41} \ln (2) \frac{1}{- 0.0559}$

Step 3

Simplify $\frac{1}{41} \ln (2)$ by moving $\frac{1}{41}$ inside the logarithm.

$\ln (2^{\frac{1}{41}}) \frac{1}{- 0.0559}$

Step 4

Divide $1$ by $- 0.0559$ .

$\ln (2^{\frac{1}{41}}) \cdot - 17.88908765$

Step 5

Multiply $\ln (2^{\frac{1}{41}}) \cdot - 17.88908765$ .

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Step 5.1

Reorder $\ln (2^{\frac{1}{41}})$ and $- 17.88908765$ .

$- 17.88908765 \cdot \ln (2^{\frac{1}{41}})$

Step 5.2

Simplify $- 17.88908765 \cdot \ln (2^{\frac{1}{41}})$ by moving $17.88908765$ inside the logarithm.

$- \ln ({(2^{\frac{1}{41}})}^{17.88908765})$

Step 6

Multiply the exponents in ${(2^{\frac{1}{41}})}^{17.88908765}$ .

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Step 6.1

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

$- \ln (2^{\frac{1}{41} \cdot 17.88908765})$

Step 6.2

Combine $\frac{1}{41}$ and $17.88908765$ .

$- \ln (2^{\frac{17.88908765}{41}})$

Step 6.3

Divide $17.88908765$ by $41$ .

$- \ln (2^{0.43631921})$

Step 7

Raise $2$ to the power of $0.43631921$ .

$- \ln (1.35314759)$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \ln (1.35314759)$

Decimal Form:

$- 0.30243343 \dots$