Graph - log base 2 of x

$- \log_{2} (x)$

Step 1

Find the asymptotes.

Set the argument of the logarithm equal to zero.

$x = 0$

The vertical asymptote occurs at $x = 0$ .

Vertical Asymptote: $x = 0$

Step 2

Find the point at $x = 1$ .

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

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

Simplify the result.

Logarithm base $2$ of $1$ is $0$ .

$f (1) = - 0$

Multiply $- 1$ by $0$ .

$f (1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 2$ .

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

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

Simplify the result.

Logarithm base $2$ of $2$ is $1$ .

$f (2) = - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$f (2) = - 1$

The final answer is $- 1$ .

$- 1$

Convert $- 1$ to decimal.

$y = - 1$

Step 4

Find the point at $x = 4$ .

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

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

Simplify the result.

Logarithm base $2$ of $4$ is $2$ .

$f (4) = - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$f (4) = - 2$

The final answer is $- 2$ .

$- 2$

Convert $- 2$ to decimal.

$y = - 2$

Step 5

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

Vertical Asymptote: $x = 0$

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

Step 6

Graph - log base 2 of x

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