Algebra Examples

$\log_{0.1} (17)$

Step 1

Rewrite $\log_{0.1} (17)$ using the change of base formula.

Tap for more steps...

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 $b = 10$ .

$\frac{\log (17)}{\log (0.1)}$

Step 2

Log base $10$ of $0.1$ is approximately $- 1$ .

$\frac{\log (17)}{- 1}$

Step 3

Rewrite $\frac{\log (17)}{- 1}$ as $\frac{1}{- 1} \log (17)$ .

$\frac{1}{- 1} \log (17)$

Step 4

Simplify $\frac{1}{- 1} \log (17)$ by moving $- \frac{1}{- 1}$ inside the logarithm.

$- \log (17^{- \frac{1}{- 1}})$

Step 5

Divide $1$ by $- 1$ .

$- \log (17^{- - 1})$

Step 6

Multiply $- 1$ by $- 1$ .

$- \log (17^{1})$

Step 7

Evaluate the exponent.

$- \log (17)$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \log (17)$

Decimal Form:

$- 1.23044892 \dots$