Pre-Algebra Examples

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

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

Step 1

Rewrite in slope-intercept form.

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Step 1.1

The slope-intercept form is

y = m x + b

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 1.2

Simplify the right side.

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Step 1.2.1

Multiply

3

$3$ by

2

$2$ .

log (3 x) = log (6 x)

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

log (3 x) = log (6 x)

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

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

$3 x = 6 x$

Step 1.4

Solve for

x

$x$ .

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Step 1.4.1

Move all terms containing

x

$x$ to the left side of the equation.

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Step 1.4.1.1

Subtract

6 x

$6 x$ from both sides of the equation.

3 x - 6 x = 0

$3 x - 6 x = 0$

Step 1.4.1.2

Subtract

6 x

$6 x$ from

3 x

$3 x$ .

- 3 x = 0

$- 3 x = 0$

- 3 x = 0

$- 3 x = 0$

Step 1.4.2

Divide each term in

- 3 x = 0

$- 3 x = 0$ by

- 3

$- 3$ and simplify.

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Step 1.4.2.1

Divide each term in

- 3 x = 0

$- 3 x = 0$ by

- 3

$- 3$ .

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

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

Step 1.4.2.2

Simplify the left side.

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Step 1.4.2.2.1

Cancel the common factor of

- 3

$- 3$ .

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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.

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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