Evaluate log base 2.2 of 22

$\log_{2.2} (22)$

Step 1

Rewrite $\log_{2.2} (22)$ using the change of base formula.

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 $0$ .

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

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

$\frac{\log (22)}{\log (2.2)}$

Step 2

Log base $10$ of $2.2$ is approximately $0.34242268$ .

$\frac{\log (22)}{0.34242268}$

Step 3

Log base $10$ of $22$ is approximately $1.34242268$ .

$\frac{1.34242268}{0.34242268}$

Step 4

Divide $1.34242268$ by $0.34242268$ .

$3.9203673$