Algebra Examples

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

Step 1

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

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

Step 2

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

Tap for more steps...

Step 2.1

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

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

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Dividing two negative values results in a positive value.

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

Step 2.2.2

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

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

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

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

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

Step 2.3.2

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

$\log (a x) = - y$

Step 3

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 $b^{y} = x$ .

$10^{- y} = a x$

Step 4

Solve for $x$ .

Tap for more steps...

Step 4.1

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

$a x = 10^{- y}$

Step 4.2

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

Tap for more steps...

Step 4.2.1

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

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

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor of $a$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor.

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

Step 4.2.2.1.2

Divide $x$ by $1$ .

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