Precalculus Examples

3 ln (5 x) = 10

$3 \ln (5 x) = 10$

Step 1

Divide each term in

3 ln (5 x) = 10

$3 \ln (5 x) = 10$ by

3

$3$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in

3 ln (5 x) = 10

$3 \ln (5 x) = 10$ by

3

$3$ .

\frac{3 ln (5 x)}{3} = \frac{10}{3}

$\frac{3 \ln (5 x)}{3} = \frac{10}{3}$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Cancel the common factor of

3

$3$ .

Tap for more steps...

Step 1.2.1.1

Cancel the common factor.

$\frac{3 \ln (5 x)}{3} = \frac{10}{3}$

Step 1.2.1.2

Divide

$\ln (5 x)$ by

$1$ .

$\ln (5 x) = \frac{10}{3}$

Step 2

To solve for

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

$e^{\ln (5 x)} = e^{\frac{10}{3}}$

Step 3

Rewrite

$\ln (5 x) = \frac{10}{3}$ 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

$b^{y} = x$ .

$e^{\frac{10}{3}} = 5 x$

Step 4

Solve for

$x$ .

Tap for more steps...

Step 4.1

Rewrite the equation as

$5 x = e^{\frac{10}{3}}$ .

$5 x = e^{\frac{10}{3}}$

Step 4.2

Divide each term in

$5 x = e^{\frac{10}{3}}$ by

$5$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in

$5 x = e^{\frac{10}{3}}$ by

$5$ .

$\frac{5 x}{5} = \frac{e^{\frac{10}{3}}}{5}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor of

$5$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{e^{\frac{10}{3}}}{5}$

Step 4.2.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{e^{\frac{10}{3}}}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{e^{\frac{10}{3}}}{5}$

Decimal Form:

$x = 5.60632497 \dots$