Calculus Examples

$\ln (y) = \frac{\ln (x^{2} - 3)}{2}$

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, $b = e$ , $x = y$ , and $y = \frac{\ln (x^{2} - 3)}{2}$ .

$b = e$

$x = y$

$y = \frac{\ln (x^{2} - 3)}{2}$

Step 2

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

$e^{\frac{\ln (x^{2} - 3)}{2}} = y$