Algebra Examples

$\log (2 x) = - 1$

Step 1

Rewrite $\log (2 x) = - 1$ 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 $b^{y} = x$ .

$10^{- 1} = 2 x$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $2 x = 10^{- 1}$ .

$2 x = 10^{- 1}$

Step 2.2

Divide each term in $2 x = 10^{- 1}$ by $2$ and simplify.

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Step 2.2.1

Divide each term in $2 x = 10^{- 1}$ by $2$ .

$\frac{2 x}{2} = \frac{10^{- 1}}{2}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{10^{- 1}}{2}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{10^{- 1}}{2}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Move $10^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$x = \frac{1}{2 \cdot 10}$

Step 2.2.3.2

Multiply $2$ by $10$ .

$x = \frac{1}{20}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{20}$

Decimal Form:

$x = 0.05$