Pre-Algebra Examples

$\log (3 x) = \log (2 \cdot (3 \cdot x))$

Step 1

Rewrite in slope-intercept form.

Tap for more steps...

Step 1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.2

Simplify the right side.

Tap for more steps...

Step 1.2.1

Multiply $3$ by $2$ .

$\log (3 x) = \log (6 x)$

Step 1.3

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

$3 x = 6 x$

Step 1.4

Solve for $x$ .

Tap for more steps...

Step 1.4.1

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

Tap for more steps...

Step 1.4.1.1

Subtract $6 x$ from both sides of the equation.

$3 x - 6 x = 0$

Step 1.4.1.2

Subtract $6 x$ from $3 x$ .

$- 3 x = 0$

Step 1.4.2

Divide each term in $- 3 x = 0$ by $- 3$ and simplify.

Tap for more steps...

Step 1.4.2.1

Divide each term in $- 3 x = 0$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{0}{- 3}$

Step 1.4.2.2

Simplify the left side.

Tap for more steps...

Step 1.4.2.2.1

Cancel the common factor of $- 3$ .

Tap for more steps...

Step 1.4.2.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{0}{- 3}$

Step 1.4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{- 3}$

Step 1.4.2.3

Simplify the right side.

Tap for more steps...

Step 1.4.2.3.1

Divide $0$ by $- 3$ .

$x = 0$

Step 1.5

Exclude the solutions that do not make $\log (3 x) = \log (6 x)$ true.

$No solution$

Step 2

The equation is not linear, so a constant slope does not exist.

Not Linear