Solve for x 2 log of x=-4

$2 \log (x) = - 4$

Step 1

Divide each term in $2 \log (x) = - 4$ by $2$ and simplify.

Divide each term in $2 \log (x) = - 4$ by $2$ .

$\frac{2 \log (x)}{2} = \frac{- 4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \log (x)}{2} = \frac{- 4}{2}$

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

$\log (x) = \frac{- 4}{2}$

Simplify the right side.

Divide $- 4$ by $2$ .

$\log (x) = - 2$

Step 2

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

$10^{- 2} = x$

Step 3

Solve for $x$ .

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

$x = 10^{- 2}$

Simplify $10^{- 2}$ .

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

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

Raise $10$ to the power of $2$ .

$x = \frac{1}{100}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{100}$

Decimal Form:

$x = 0.01$

Solve for x 2 log of x=-4

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