Calculus Examples

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

Step 1

To solve for

$x$ , rewrite the equation using properties of logarithms.

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

Step 2

Rewrite

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

$b^{y} = x$ .

$e^{\frac{1}{2}} = x$

Step 3

Rewrite the equation as

$x = e^{\frac{1}{2}}$ .

$x = e^{\frac{1}{2}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = e^{\frac{1}{2}}$

Decimal Form:

$x = 1.64872127 \dots$

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

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