Solve for x y=- log of a*x

$y = - \log (a \cdot x)$

Rewrite the equation as $- \log (a \cdot x) = y$ .

$- \log (a \cdot x) = y$

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

Divide each term in $- \log (a \cdot x) = y$ by $- 1$ .

$\frac{- \log (a \cdot x)}{- 1} = \frac{y}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\log (a \cdot x)}{1} = \frac{y}{- 1}$

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

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

Simplify the right side.

Move the negative one from the denominator of $\frac{y}{- 1}$ .

$\log (a x) = - 1 \cdot y$

Rewrite $- 1 \cdot y$ as $- y$ .

$\log (a x) = - y$

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

$10^{- y} = a x$

Solve for $x$ .

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

$a x = 10^{- y}$

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

Divide each term in $a x = 10^{- y}$ by $a$ .

$\frac{a x}{a} = \frac{10^{- y}}{a}$

Simplify the left side.

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{a x}{a} = \frac{10^{- y}}{a}$

Divide $x$ by $1$ .

$x = \frac{10^{- y}}{a}$

Solve for x y=- log of a*x

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