Solve for x log of 4x=-1

$\log (4 x) = - 1$

Step 1

Rewrite $\log (4 x) = - 1$ 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 $b^{y} = x$ .

$10^{- 1} = 4 x$

Step 2

Solve for $x$ .

Rewrite the equation as $4 x = 10^{- 1}$ .

$4 x = 10^{- 1}$

Divide each term in $4 x = 10^{- 1}$ by $4$ and simplify.

Divide each term in $4 x = 10^{- 1}$ by $4$ .

$\frac{4 x}{4} = \frac{10^{- 1}}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{10^{- 1}}{4}$

Divide $x$ by $1$ .

$x = \frac{10^{- 1}}{4}$

Simplify the right side.

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

$x = \frac{1}{4 \cdot 10}$

Multiply $4$ by $10$ .

$x = \frac{1}{40}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{40}$

Decimal Form:

$x = 0.025$

Solve for x log of 4x=-1

Related Questions

Support LCMGCF.com by disabling your adblocker.