Solve for x natural log of x+ natural log of 4=2

$\ln (x) + \ln (4) = 2$

Step 1

Simplify the left side.

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\ln (x \cdot 4) = 2$

Move $4$ to the left of $x$ .

$\ln (4 x) = 2$

Step 2

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

$e^{\ln (4 x)} = e^{2}$

Step 3

Rewrite $\ln (4 x) = 2$ 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 $b^{y} = x$ .

$e^{2} = 4 x$

Step 4

Solve for $x$ .

Rewrite the equation as $4 x = e^{2}$ .

$4 x = e^{2}$

Divide each term in $4 x = e^{2}$ by $4$ and simplify.

Divide each term in $4 x = e^{2}$ by $4$ .

$\frac{4 x}{4} = \frac{e^{2}}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{e^{2}}{4}$

Divide $x$ by $1$ .

$x = \frac{e^{2}}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{e^{2}}{4}$

Decimal Form:

$x = 1.84726402 \dots$

Solve for x natural log of x+ natural log of 4=2

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