Algebra Examples

$\log (x) = - 5$

Step 1

Rewrite $\log (x) = - 5$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$10^{- 5} = x$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $x = 10^{- 5}$ .

$x = 10^{- 5}$

Step 2.2

Simplify $10^{- 5}$ .

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Step 2.2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$x = \frac{1}{10^{5}}$

Step 2.2.2

Raise $10$ to the power of $5$ .

$x = \frac{1}{100000}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{100000}$

Decimal Form:

$x = 1 \cdot 10^{- 5}$