Precalculus Examples

$\log_{4} (16^{1.2}) + 4^{2 \log_{4} (20)}$

Step 1

Simplify each term.

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Step 1.1

Raise $16$ to the power of $1.2$ .

$\log_{4} (27.85761802) + 4^{2 \log_{4} (20)}$

Step 1.2

Log base $4$ of $27.85761802$ is approximately $2.4$ .

$2.4 + 4^{2 \log_{4} (20)}$

Step 1.3

Simplify $2 \log_{4} (20)$ by moving $2$ inside the logarithm.

$2.4 + 4^{\log_{4} (20^{2})}$

Step 1.4

Exponentiation and log are inverse functions.

$2.4 + 20^{2}$

Step 1.5

Raise $20$ to the power of $2$ .

$2.4 + 400$

Step 2

Add $2.4$ and $400$ .

$402.4$