Precalculus Examples

$\log_{16} (2^{1.9}) + e^{3 \ln (10)}$

Step 1

Expand $\log_{16} (2^{1.9})$ by moving $1.9$ outside the logarithm.

$1.9 \log_{16} (2) + e^{3 \ln (10)}$

Step 2

Logarithm base $16$ of $2$ is $\frac{1}{4}$ .

$1.9 (\frac{1}{4}) + e^{3 \ln (10)}$

Step 3

Combine $1.9$ and $\frac{1}{4}$ .

$\frac{1.9}{4} + e^{3 \ln (10)}$

Step 4

Divide $1.9$ by $4$ .

$0.475 + e^{3 \ln (10)}$

Step 5

Simplify each term.

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Simplify $3 \ln (10)$ by moving $3$ inside the logarithm.

$0.475 + e^{\ln (10^{3})}$

Exponentiation and log are inverse functions.

$0.475 + 10^{3}$

Raise $10$ to the power of $3$ .

$0.475 + 1000$

Step 6

Add $0.475$ and $1000$ .

$1000.475$