Graph y=- log base 4 of x

$y = - \log_{4} (x)$

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.

$f (1) = - \log_{4} (1)$

Simplify the result.

Logarithm base $4$ 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 $x = 4$ .

Replace the variable $x$ with $4$ in the expression.

$f (4) = - \log_{4} (4)$

Simplify the result.

Logarithm base $4$ of $4$ is $1$ .

$f (4) = - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$f (4) = - 1$

The final answer is $- 1$ .

$- 1$

Convert $- 1$ to decimal.

$y = - 1$

Find the point at $x = 2$ .

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

$f (2) = - \log_{4} (2)$

Simplify the result.

Logarithm base $4$ of $2$ is $\frac{1}{2}$ .

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

The final answer is $- \frac{1}{2}$ .

$- \frac{1}{2}$

Convert $- \frac{1}{2}$ to decimal.

$y = - 0.5$

The log function can be graphed using the vertical asymptote at $x = 0$ and the points $(1, 0), (4, - 1), (2, - 0.5)$ .

Vertical Asymptote: $x = 0$

$\begin{array}{c} x & y \\ 1 & 0 \\ 2 & - 0.5 \\ 4 & - 1 \end{array}$