Calculus Examples

$\frac{1 - \ln (x)}{x^{2}} = 0$

Step 1

Set the numerator equal to zero.

$1 - \ln (x) = 0$

Step 2

Solve the equation for $x$ .

Tap for more steps...

Step 2.1

Subtract $1$ from both sides of the equation.

$- \ln (x) = - 1$

Step 2.2

Divide each term in $- \ln (x) = - 1$ by $- 1$ and simplify.

Tap for more steps...

Step 2.2.1

Divide each term in $- \ln (x) = - 1$ by $- 1$ .

$\frac{- \ln (x)}{- 1} = \frac{- 1}{- 1}$

Step 2.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.2.1

Dividing two negative values results in a positive value.

$\frac{\ln (x)}{1} = \frac{- 1}{- 1}$

Step 2.2.2.2

Divide $\ln (x)$ by $1$ .

$\ln (x) = \frac{- 1}{- 1}$

Step 2.2.3

Simplify the right side.

Tap for more steps...

Step 2.2.3.1

Divide $- 1$ by $- 1$ .

$\ln (x) = 1$

Step 2.3

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

$e^{\ln (x)} = e^{1}$

Step 2.4

Rewrite $\ln (x) = 1$ 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 $b^{y} = x$ .

$e^{1} = x$

Step 2.5

Rewrite the equation as $x = e^{1}$ .

$x = e$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = e$

Decimal Form:

$x = 2.71828182 \dots$