Calculus Examples

$e^{\ln (x)} = 4$

Step 1

Divide both sides by $e^{\ln (x)}$ to remove it from the front of the logarithm.

$\frac{e^{\ln (x)}}{e^{\ln (x)}} = \frac{4}{e^{\ln (x)}}$

Step 2

Simplify each side of the equation.

$= \frac{4}{x}$

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, $b = 10$ , $x =$ , and $y = \frac{4}{x}$ .

$b = 10$

$x =$

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

Step 4

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

$10^{\frac{4}{x}} =$