Precalculus Examples

$(\frac{\ln (\frac{1}{2})}{1599}) \cdot 1000$

Step 1

Rewrite $\frac{\ln (\frac{1}{2})}{1599}$ as $\frac{1}{1599} \ln (\frac{1}{2})$ .

$\frac{1}{1599} \ln (\frac{1}{2}) \cdot 1000$

Step 2

Simplify $\frac{1}{1599} \ln (\frac{1}{2})$ by moving $\frac{1}{1599}$ inside the logarithm.

$\ln ({(\frac{1}{2})}^{\frac{1}{1599}}) \cdot 1000$

Step 3

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

$\ln (\frac{1^{\frac{1}{1599}}}{2^{\frac{1}{1599}}}) \cdot 1000$

Step 4

One to any power is one.

$\ln (\frac{1}{2^{\frac{1}{1599}}}) \cdot 1000$

Step 5

Multiply $\ln (\frac{1}{2^{\frac{1}{1599}}}) \cdot 1000$ .

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Step 5.1

Reorder $\ln (\frac{1}{2^{\frac{1}{1599}}})$ and $1000$ .

$1000 \cdot \ln (\frac{1}{2^{\frac{1}{1599}}})$

Step 5.2

Simplify $1000 \cdot \ln (\frac{1}{2^{\frac{1}{1599}}})$ by moving $1000$ inside the logarithm.

$\ln ({(\frac{1}{2^{\frac{1}{1599}}})}^{1000})$

Step 6

Apply the product rule to $\frac{1}{2^{\frac{1}{1599}}}$ .

$\ln (\frac{1^{1000}}{{(2^{\frac{1}{1599}})}^{1000}})$

Step 7

One to any power is one.

$\ln (\frac{1}{{(2^{\frac{1}{1599}})}^{1000}})$

Step 8

Multiply the exponents in ${(2^{\frac{1}{1599}})}^{1000}$ .

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Step 8.1

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

$\ln (\frac{1}{2^{\frac{1}{1599} \cdot 1000}})$

Step 8.2

Combine $\frac{1}{1599}$ and $1000$ .

$\ln (\frac{1}{2^{\frac{1000}{1599}}})$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\ln (\frac{1}{2^{\frac{1000}{1599}}})$

Decimal Form:

$- 0.43348791 \dots$