Precalculus Examples

$3 + 2 \ln (x) = 10$

Step 1

Move all terms not containing $\ln (x)$ to the right side of the equation.

Tap for more steps...

Step 1.1

Subtract $3$ from both sides of the equation.

$2 \ln (x) = 10 - 3$

Step 1.2

Subtract $3$ from $10$ .

$2 \ln (x) = 7$

Step 2

Divide each term in $2 \ln (x) = 7$ by $2$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $2 \ln (x) = 7$ by $2$ .

$\frac{2 \ln (x)}{2} = \frac{7}{2}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{2 \ln (x)}{2} = \frac{7}{2}$

Step 2.2.1.2

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

$\ln (x) = \frac{7}{2}$

Step 3

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

$e^{\ln (x)} = e^{\frac{7}{2}}$

Step 4

Rewrite $\ln (x) = \frac{7}{2}$ 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 $b^{y} = x$ .

$e^{\frac{7}{2}} = x$

Step 5

Rewrite the equation as $x = e^{\frac{7}{2}}$ .

$x = e^{\frac{7}{2}}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = e^{\frac{7}{2}}$

Decimal Form:

$x = 33.11545195 \dots$