Precalculus Examples

$\log_{1.099} (\sqrt{{1.099}^{3}})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{{1.099}^{3}}$ as ${1.099}^{\frac{3}{2}}$ .

$\log_{1.099} ({1.099}^{\frac{3}{2}})$

Step 2

Expand $\log_{1.099} ({1.099}^{\frac{3}{2}})$ by moving $\frac{3}{2}$ outside the logarithm.

$\frac{3}{2} \log_{1.099} (1.099)$

Step 3

Log base $1.099$ of $1.099$ is approximately $1$ .

$\frac{3}{2} \cdot 1$

Step 4

Multiply $\frac{3}{2}$ by $1$ .

$\frac{3}{2}$