Precalculus Examples

$\log (\frac{15 x + 40}{2 x + 5}) = 1$

Step 1

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, $b = 10$ , $x = \frac{15 x + 40}{2 x + 5}$ , and $y = 1$ .

$b = 10$

$x = \frac{15 x + 40}{2 x + 5}$

$y = 1$

Step 2

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

$10 = \frac{15 x + 40}{2 x + 5}$