Graph f(x)=5 natural log of x

$f (x) = 5 \ln (x)$

Find the asymptotes.

Set the argument of the logarithm equal to zero.

$x^{5} = 0$

Solve for $x$ .

Take the 5th root of both sides of the equation to eliminate the exponent on the left side.

$x = \sqrt[5]{0}$

Simplify $\sqrt[5]{0}$ .

Rewrite $0$ as $0^{5}$ .

$x = \sqrt[5]{0^{5}}$

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

$x = 0$

The vertical asymptote occurs at $x = 0$ .

Vertical Asymptote: $x = 0$

Find the point at $x = 1$ .

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

$f (1) = 5 \ln (1)$

Simplify the result.

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

$f (1) = 5 \cdot 0$

Multiply $5$ by $0$ .

$f (1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = 2$ .

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

$f (2) = 5 \ln (2)$

Simplify the result.

Simplify $5 \ln (2)$ by moving $5$ inside the logarithm.

$f (2) = \ln (2^{5})$

Raise $2$ to the power of $5$ .

$f (2) = \ln (32)$

The final answer is $\ln (32)$ .

$\ln (32)$

Convert $\ln (32)$ to decimal.

$y = 3.4657359$

Find the point at $x = 3$ .

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

$f (3) = 5 \ln (3)$

Simplify the result.

Simplify $5 \ln (3)$ by moving $5$ inside the logarithm.

$f (3) = \ln (3^{5})$

Raise $3$ to the power of $5$ .

$f (3) = \ln (243)$

The final answer is $\ln (243)$ .

$\ln (243)$

Convert $\ln (243)$ to decimal.

$y = 5.49306144$

The log function can be graphed using the vertical asymptote at $x = 0$ and the points $(1, 0), (2, 3.4657359), (3, 5.49306144)$ .

Vertical Asymptote: $x = 0$

$\begin{array}{c} x & y \\ 1 & 0 \\ 2 & 3.466 \\ 3 & 5.493 \end{array}$

Graph f(x)=5 natural log of x

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