Precalculus Examples

$\frac{2000^{\ln (\frac{19}{10}) \cdot 5}}{2}$

Step 1

Multiply $\ln (\frac{19}{10}) \cdot 5$ .

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Step 1.1

Reorder $\ln (\frac{19}{10})$ and $5$ .

$\frac{2000^{5 \cdot \ln (\frac{19}{10})}}{2}$

Step 1.2

Simplify $5 \cdot \ln (\frac{19}{10})$ by moving $5$ inside the logarithm.

$\frac{2000^{\ln ({(\frac{19}{10})}^{5})}}{2}$

Step 2

Apply the product rule to $\frac{19}{10}$ .

$\frac{2000^{\ln (\frac{19^{5}}{10^{5}})}}{2}$

Step 3

Raise $19$ to the power of $5$ .

$\frac{2000^{\ln (\frac{2476099}{10^{5}})}}{2}$

Step 4

Raise $10$ to the power of $5$ .

$\frac{2000^{\ln (\frac{2476099}{100000})}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{2000^{\ln (\frac{2476099}{100000})}}{2}$

Decimal Form:

$19627485255.3441$