Algebra Examples

$\log_{3} (x + 12) = \log_{3} (5 x)$

Step 1

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

$x + 12 = 5 x$

Step 2

Solve for $x$ .

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Step 2.1

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

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Step 2.1.1

Subtract $5 x$ from both sides of the equation.

$x + 12 - 5 x = 0$

Step 2.1.2

Subtract $5 x$ from $x$ .

$- 4 x + 12 = 0$

Step 2.2

Subtract $12$ from both sides of the equation.

$- 4 x = - 12$

Step 2.3

Divide each term in $- 4 x = - 12$ by $- 4$ and simplify.

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Step 2.3.1

Divide each term in $- 4 x = - 12$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 12}{- 4}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 4$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 12}{- 4}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 12}{- 4}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $- 12$ by $- 4$ .

$x = 3$