Precalculus Examples

$\frac{125 x}{12} = 200 \log (\frac{9 x}{24} + 1)$

Step 1

Divide both sides by $200$ to remove it from the front of the logarithm.

$\frac{\frac{125 x}{12}}{200} = \frac{200 \log (\frac{9 x}{24} + 1)}{200}$

Step 2

Simplify each side of the equation.

$\frac{5 x}{96} = \log (\frac{9 x}{24} + 1)$

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, $b = 10$ , $x = \frac{9 x}{24} + 1$ , and $y = \frac{5 x}{96}$ .

$b = 10$

$x = \frac{9 x}{24} + 1$

$y = \frac{5 x}{96}$

Step 4

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

$10^{\frac{5 x}{96}} = \frac{9 x}{24} + 1$