Pre-Algebra Examples

$3 \log (x - 2) = 4$

Step 1

Divide both sides by $3$ to remove it from the front of the logarithm.

$\frac{3 \log (x - 2)}{3} = \frac{4}{3}$

Step 2

Simplify each side of the equation.

$\log (x - 2) = \frac{4}{3}$

Step 3

For logarithmic equations, $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ such that $x > 0$ , $b > 0$ , and $b \neq 1$ . In this case, $b = 10$ , $x = x - 2$ , and $y = \frac{4}{3}$ .

$b = 10$

$x = x - 2$

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

Step 4

Substitute the values of $b$ , $x$ , and $y$ into the equation $b^{y} = x$ .

$10^{\frac{4}{3}} = x - 2$