Precalculus Examples

$11 \ln (2 x) = 7$

Step 1

Divide both sides by $11$ to remove it from the front of the logarithm.

$\frac{11 \ln (2 x)}{11} = \frac{7}{11}$

Step 2

Simplify each side of the equation.

$\ln (2 x) = \frac{7}{11}$

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, $b = e$ , $x = 2 x$ , and $y = \frac{7}{11}$ .

$b = e$

$x = 2 x$

$y = \frac{7}{11}$

Step 4

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

$e^{\frac{7}{11}} = 2 x$