Precalculus Examples

$e^{\ln (20) - \ln (5)}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $\ln (20)$ as $\ln (2^{2} \cdot 5)$ .

$e^{\ln (2^{2} \cdot 5) - \ln (5)}$

Step 1.2

Rewrite $\ln (2^{2} \cdot 5)$ as $\ln (2^{2}) + \ln (5)$ .

$e^{\ln (2^{2}) + \ln (5) - \ln (5)}$

Step 1.3

Expand $\ln (2^{2})$ by moving $2$ outside the logarithm.

$e^{2 \ln (2) + \ln (5) - \ln (5)}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $\ln (5)$ from $\ln (5)$ .

$e^{2 \ln (2) + 0}$

Step 2.2

Add $2 \ln (2)$ and $0$ .

$e^{2 \ln (2)}$

Step 3

Simplify $2 \ln (2)$ by moving $2$ inside the logarithm.

$e^{\ln (2^{2})}$

Step 4

Exponentiation and log are inverse functions.

$2^{2}$

Step 5

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

$4$