Precalculus Examples

$50000^{\frac{\ln (2)}{23} \cdot (24)}$

Step 1

Rewrite $\frac{\ln (2)}{23}$ as $\frac{1}{23} \ln (2)$ .

$50000^{\frac{1}{23} \ln (2) \cdot 24}$

Step 2

Simplify $\frac{1}{23} \ln (2)$ by moving $\frac{1}{23}$ inside the logarithm.

$50000^{\ln (2^{\frac{1}{23}}) \cdot 24}$

Step 3

Multiply $\ln (2^{\frac{1}{23}}) \cdot 24$ .

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Step 3.1

Reorder $\ln (2^{\frac{1}{23}})$ and $24$ .

$50000^{24 \cdot \ln (2^{\frac{1}{23}})}$

Step 3.2

Simplify $24 \cdot \ln (2^{\frac{1}{23}})$ by moving $24$ inside the logarithm.

$50000^{\ln ({(2^{\frac{1}{23}})}^{24})}$

Step 4

Multiply the exponents in ${(2^{\frac{1}{23}})}^{24}$ .

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Step 4.1

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

$50000^{\ln (2^{\frac{1}{23} \cdot 24})}$

Step 4.2

Combine $\frac{1}{23}$ and $24$ .

$50000^{\ln (2^{\frac{24}{23}})}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$50000^{\ln (2^{\frac{24}{23}})}$

Decimal Form:

$2504.32038550 \dots$