Finite Math Examples

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

Step 1

Simplify the right side.

Tap for more steps...

Step 1.1

Simplify $\log (2) + \log (x + 2)$ .

Tap for more steps...

Step 1.1.1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

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

Step 1.1.2

Apply the distributive property.

$\log (5 x) = \log (2 x + 2 \cdot 2)$

Step 1.1.3

Multiply $2$ by $2$ .

$\log (5 x) = \log (2 x + 4)$

Step 2

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

$5 x = 2 x + 4$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Subtract $2 x$ from both sides of the equation.

$5 x - 2 x = 4$

Step 3.1.2

Subtract $2 x$ from $5 x$ .

$3 x = 4$

Step 3.2

Divide each term in $3 x = 4$ by $3$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $3 x = 4$ by $3$ .

$\frac{3 x}{3} = \frac{4}{3}$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{4}{3}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{4}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{3}$

Decimal Form:

$x = 1.\overline{3}$

Mixed Number Form:

$x = 1 \frac{1}{3}$