Finite Math Examples

$- 5 + 6 \ln (x) = 0$

Step 1

Add $5$ to both sides of the equation.

$6 \ln (x) = 5$

Step 2

Divide each term in $6 \ln (x) = 5$ by $6$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $6 \ln (x) = 5$ by $6$ .

$\frac{6 \ln (x)}{6} = \frac{5}{6}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{6 \ln (x)}{6} = \frac{5}{6}$

Step 2.2.1.2

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

$\ln (x) = \frac{5}{6}$

Step 3

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

$e^{\ln (x)} = e^{\frac{5}{6}}$

Step 4

Rewrite $\ln (x) = \frac{5}{6}$ 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 $b^{y} = x$ .

$e^{\frac{5}{6}} = x$

Step 5

Rewrite the equation as $x = e^{\frac{5}{6}}$ .

$x = e^{\frac{5}{6}}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = e^{\frac{5}{6}}$

Decimal Form:

$x = 2.30097589 \dots$