Solve for x natural log of 3x=1

$\ln (3 x) = 1$

Step 1

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

$e^{\ln (3 x)} = e^{1}$

Step 2

Rewrite $\ln (3 x) = 1$ 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 $b^{y} = x$ .

$e^{1} = 3 x$

Step 3

Solve for $x$ .

Rewrite the equation as $3 x = e^{1}$ .

$3 x = e$

Divide each term in $3 x = e^{1}$ by $3$ and simplify.

Divide each term in $3 x = e^{1}$ by $3$ .

$\frac{3 x}{3} = \frac{e^{1}}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{e^{1}}{3}$

Divide $x$ by $1$ .

$x = \frac{e^{1}}{3}$

Simplify the right side.

Simplify.

$x = \frac{e}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{e}{3}$

Decimal Form:

$x = 0.90609394 \dots$

Solve for x natural log of 3x=1

Related Questions

Support LCMGCF.com by disabling your adblocker.