Precalculus Examples

$x (\ln (\frac{3}{4}) + \ln (5)) = \ln (5)$

Step 1

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

$\frac{x (\ln (\frac{3}{4}) + \ln (5))}{x} = \frac{\ln (5)}{x}$

Step 2

Simplify each side of the equation.

$\ln (\frac{3}{4}) + \ln (5) = \frac{\ln (5)}{x}$

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, $b = e$ , $x =$ , and $y = \frac{\ln (5)}{x}$ .

$b = e$

$x =$

$y = \frac{\ln (5)}{x}$

Step 4

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

$e^{\frac{\ln (5)}{x}} =$