Algebra Examples

$2 \log (x) = - 1$

Step 1

Divide each term in $2 \log (x) = - 1$ by $2$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in $2 \log (x) = - 1$ by $2$ .

$\frac{2 \log (x)}{2} = \frac{- 1}{2}$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.1.1

Cancel the common factor.

$\frac{2 \log (x)}{2} = \frac{- 1}{2}$

Step 1.2.1.2

Divide $\log (x)$ by $1$ .

$\log (x) = \frac{- 1}{2}$

Step 1.3

Simplify the right side.

Tap for more steps...

Step 1.3.1

Move the negative in front of the fraction.

$\log (x) = - \frac{1}{2}$

Step 2

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

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

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

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

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

Step 3.2

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.31622776 \dots$