Graph log base 2 of x

Problem

y=(log_2)(x)

Solution

1. Identify the domain, which consists of all positive real numbers because the argument of a logarithm must be greater than zero.

x>0

2. Determine the vertical asymptote by setting the argument of the logarithm to zero.

x=0

3. Find the x-intercept by setting y=0 and solving for x

(log_2)(x)=0⇒x=2=1

4. Calculate key points to determine the shape of the curve by choosing powers of the base.

If *x=2,y=(log_2)(2)=1

If *x=4,y=(log_2)(4)=2

If *x=1/2,y=(log_2)(1/2)=−1

5. Sketch the curve passing through the points (0.5,−1) (1,0) (2,1) and (4,2) ensuring the graph approaches the y-axis as x approaches 0 from the right.

Final Answer

y=(log_2)(x)

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