Basic Math Examples

$y = \ln (t^{2})$

Step 1

Rewrite the equation as $\ln (t^{2}) = y$ .

$\ln (t^{2}) = y$

Step 2

To solve for $t$ , rewrite the equation using properties of logarithms.

$e^{\ln (t^{2})} = e^{y}$

Step 3

Rewrite $\ln (t^{2}) = y$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$e^{y} = t^{2}$

Step 4

Solve for $t$ .

Tap for more steps...

Rewrite the equation as $t^{2} = e^{y}$ .

$t^{2} = e^{y}$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$t = \pm \sqrt{e^{y}}$

The complete solution is the result of both the positive and negative portions of the solution.

Tap for more steps...

First, use the positive value of the $\pm$ to find the first solution.

$t = \sqrt{e^{y}}$

Next, use the negative value of the $\pm$ to find the second solution.

$t = - \sqrt{e^{y}}$

The complete solution is the result of both the positive and negative portions of the solution.

$t = \sqrt{e^{y}}$

$t = - \sqrt{e^{y}}$

$t = \sqrt{e^{y}}$

$t = - \sqrt{e^{y}}$

$t = \sqrt{e^{y}}$

$t = - \sqrt{e^{y}}$