Graph f(x)=- log base 2/5 of x

$f (x) = - \log_{\frac{2}{5}} (x)$

Find the asymptotes.

Set the argument of the logarithm equal to zero.

$x = 0$

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.

$f (1) = - \log_{\frac{2}{5}} (1)$

Simplify the result.

Logarithm base $\frac{2}{5}$ of $1$ is $0$ .

$f (1) = - 0$

Multiply $- 1$ 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.

$f (2) = - \log_{\frac{2}{5}} (2)$

The final answer is $- \log_{\frac{2}{5}} (2)$ .

$- \log_{\frac{2}{5}} (2)$

Convert $- \log_{\frac{2}{5}} (2)$ to decimal.

$y = 0.75647079$

Find the point at $x = 3$ .

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

$f (3) = - \log_{\frac{2}{5}} (3)$

The final answer is $- \log_{\frac{2}{5}} (3)$ .

$- \log_{\frac{2}{5}} (3)$

Convert $- \log_{\frac{2}{5}} (3)$ to decimal.

$y = 1.19897784$

The log function can be graphed using the vertical asymptote at $x = 0$ and the points $(1, 0), (2, 0.75647079), (3, 1.19897784)$ .

Vertical Asymptote: $x = 0$

$\begin{array}{c} x & y \\ 1 & 0 \\ 2 & 0.756 \\ 3 & 1.199 \end{array}$