Solve for x 5 natural log of x=10

$5 \ln (x) = 10$

Step 1

Divide each term in $5 \ln (x) = 10$ by $5$ and simplify.

Divide each term in $5 \ln (x) = 10$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

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

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

Simplify the right side.

Divide $10$ by $5$ .

$\ln (x) = 2$

Step 2

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

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

Step 3

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

$e^{2} = x$

Step 4

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

$x = e^{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = e^{2}$

Decimal Form:

$x = 7.38905609 \dots$

Solve for x 5 natural log of x=10

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