Find All Complex Solutions log of 5x=-1

$\log (5 x) = - 1$

Rewrite $\log (5 x) = - 1$ 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 $b^{y} = x$ .

$10^{- 1} = 5 x$

Solve for $x$ .

Rewrite the equation as $5 x = 10^{- 1}$ .

$5 x = 10^{- 1}$

Divide each term in $5 x = 10^{- 1}$ by $5$ and simplify.

Divide each term in $5 x = 10^{- 1}$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

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

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

Multiply $5$ by $10$ .

$x = \frac{1}{50}$

Find All Complex Solutions log of 5x=-1

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