Precalculus Examples

$\log (5 x + 6) = \log (x - 2)$

Step 1

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$5 x + 6 = x - 2$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 2.1.1

Subtract $x$ from both sides of the equation.

$5 x + 6 - x = - 2$

Step 2.1.2

Subtract $x$ from $5 x$ .

$4 x + 6 = - 2$

Step 2.2

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 2.2.1

Subtract $6$ from both sides of the equation.

$4 x = - 2 - 6$

Step 2.2.2

Subtract $6$ from $- 2$ .

$4 x = - 8$

Step 2.3

Divide each term in $4 x = - 8$ by $4$ and simplify.

Tap for more steps...

Step 2.3.1

Divide each term in $4 x = - 8$ by $4$ .

$\frac{4 x}{4} = \frac{- 8}{4}$

Step 2.3.2

Simplify the left side.

Tap for more steps...

Step 2.3.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.3.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 8}{4}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 8}{4}$

Step 2.3.3

Simplify the right side.

Tap for more steps...

Step 2.3.3.1

Divide $- 8$ by $4$ .

$x = - 2$

Step 3

Exclude the solutions that do not make $\log (5 x + 6) = \log (x - 2)$ true.

$No solution$