Precalculus Examples

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

Step 1

Raise $1.099$ to the power of $3$ .

$\log_{1.099} (\sqrt{1.32737329})$

Step 2

Rewrite $\log_{1.099} (\sqrt{1.32737329})$ using the change of base formula.

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Step 2.1

The change of base rule can be used if $a$ and $b$ are greater than $0$ and not equal to $1$ , and $x$ is greater than $0$ .

$\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}$

Step 2.2

Substitute in values for the variables in the change of base formula, using $b = 10$ .

$\frac{\log (\sqrt{1.32737329})}{\log (1.099)}$

Step 3

Log base $10$ of $1.099$ is approximately $0.04099769$ .

$\frac{\log (\sqrt{1.32737329})}{0.04099769}$

Step 4

Evaluate the root.

$\frac{\log (1.15211687)}{0.04099769}$

Step 5

Log base $10$ of $1.15211687$ is approximately $0.06149653$ .

$\frac{0.06149653}{0.04099769}$

Step 6

Divide $0.06149653$ by $0.04099769$ .

$1.5$