Precalculus Examples

$\log_{0.2} (10)$

Step 1

Rewrite $\log_{0.2} (10)$ using the change of base formula.

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Step 1.1

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 1.2

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

$\frac{\log (10)}{\log (0.2)}$

Step 2

Logarithm base $10$ of $10$ is $1$ .

$\frac{1}{\log (0.2)}$

Step 3

Log base $10$ of $0.2$ is approximately $- 0.69897$ .

$\frac{1}{- 0.69897}$

Step 4

Divide $1$ by $- 0.69897$ .

$- 1.43067655$