Graph f(x)=2 natural log of x

$f (x) = 2 \ln (x)$

Step 1

Find the asymptotes.

Set the argument of the logarithm equal to zero.

$x^{2} = 0$

Solve for $x$ .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$

The vertical asymptote occurs at $x = 0$ .

Vertical Asymptote: $x = 0$

Step 2

Find the point at $x = 1$ .

Replace the variable $x$ with $1$ in the expression.

$f (1) = 2 \ln (1)$

Simplify the result.

The natural logarithm of $1$ is $0$ .

$f (1) = 2 \cdot 0$

Multiply $2$ by $0$ .

$f (1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 2$ .

Replace the variable $x$ with $2$ in the expression.

$f (2) = 2 \ln (2)$

Simplify the result.

Simplify $2 \ln (2)$ by moving $2$ inside the logarithm.

$f (2) = \ln (2^{2})$

Raise $2$ to the power of $2$ .

$f (2) = \ln (4)$

The final answer is $\ln (4)$ .

$\ln (4)$

Convert $\ln (4)$ to decimal.

$y = 1.38629436$

Step 4

Find the point at $x = 3$ .

Replace the variable $x$ with $3$ in the expression.

$f (3) = 2 \ln (3)$

Simplify the result.

Simplify $2 \ln (3)$ by moving $2$ inside the logarithm.

$f (3) = \ln (3^{2})$

Raise $3$ to the power of $2$ .

$f (3) = \ln (9)$

The final answer is $\ln (9)$ .

$\ln (9)$

Convert $\ln (9)$ to decimal.

$y = 2.19722457$

Step 5

The log function can be graphed using the vertical asymptote at $x = 0$ and the points $(1, 0), (2, 1.38629436), (3, 2.19722457)$ .

Vertical Asymptote: $x = 0$

$\begin{array}{c} x & y \\ 1 & 0 \\ 2 & 1.386 \\ 3 & 2.197 \end{array}$

Step 6

Graph f(x)=2 natural log of x

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