Algebra Examples

$\log_{3} (3 x + 2) = \log_{3} (4 x - 6)$

Step 1

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

$3 x + 2 = 4 x - 6$

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 $4 x$ from both sides of the equation.

$3 x + 2 - 4 x = - 6$

Step 2.1.2

Subtract $4 x$ from $3 x$ .

$- x + 2 = - 6$

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 $2$ from both sides of the equation.

$- x = - 6 - 2$

Step 2.2.2

Subtract $2$ from $- 6$ .

$- x = - 8$

Step 2.3

Divide each term in $- x = - 8$ by $- 1$ and simplify.

Tap for more steps...

Step 2.3.1

Divide each term in $- x = - 8$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 8}{- 1}$

Step 2.3.2

Simplify the left side.

Tap for more steps...

Step 2.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 8}{- 1}$

Step 2.3.2.2

Divide $x$ by $1$ .

$x = \frac{- 8}{- 1}$

Step 2.3.3

Simplify the right side.

Tap for more steps...

Step 2.3.3.1

Divide $- 8$ by $- 1$ .

$x = 8$