Algebra Examples

$f (x) = \log (\frac{1}{2} x)$

Step 1

Find the asymptotes.

Tap for more steps...

Step 1.1

Set the argument of the logarithm equal to zero.

$\frac{x}{2} = 0$

Step 1.2

Set the numerator equal to zero.

$x = 0$

Step 1.3

The vertical asymptote occurs at $x = 0$ .

Vertical Asymptote: $x = 0$

Step 2

Find the point at $x = 2$ .

Tap for more steps...

Step 2.1

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

$f (2) = \log (\frac{1}{2} \cdot (2))$

Step 2.2

Simplify the result.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$f (2) = \log (\frac{1}{2} \cdot 2)$

Step 2.2.1.2

Rewrite the expression.

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

Step 2.2.2

Logarithm base $10$ of $1$ is $0$ .

$f (2) = 0$

Step 2.2.3

The final answer is $0$ .

$0$

Step 2.3

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 1$ .

Tap for more steps...

Step 3.1

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

$f (1) = \log (\frac{1}{2} \cdot (1))$

Step 3.2

Simplify the result.

Tap for more steps...

Step 3.2.1

Multiply $\frac{1}{2}$ by $1$ .

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

Step 3.2.2

The final answer is $\log (\frac{1}{2})$ .

$\log (\frac{1}{2})$

Step 3.3

Convert $\log (\frac{1}{2})$ to decimal.

$y = - 0.30102999$

Step 4

Find the point at $x = 3$ .

Tap for more steps...

Step 4.1

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

$f (3) = \log (\frac{1}{2} \cdot (3))$

Step 4.2

Simplify the result.

Tap for more steps...

Step 4.2.1

Combine $\frac{1}{2}$ and $3$ .

$f (3) = \log (\frac{3}{2})$

Step 4.2.2

The final answer is $\log (\frac{3}{2})$ .

$\log (\frac{3}{2})$

Step 4.3

Convert $\log (\frac{3}{2})$ to decimal.

$y = 0.17609125$

Step 5

The log function can be graphed using the vertical asymptote at $x = 0$ and the points $(2, 0), (1, - 0.30102999), (3, 0.17609125)$ .

Vertical Asymptote: $x = 0$

$\begin{array}{c} x & y \\ 1 & - 0.301 \\ 2 & 0 \\ 3 & 0.176 \end{array}$

Step 6