Graph log base 2 of x=y

Problem

(log_2)(x)=y

Solution

1. Identify the function as a logarithmic function with base 2

2. Convert the logarithmic equation to its equivalent exponential form to find coordinates more easily.

x=2

3. Select values for y to determine corresponding x values, since x must be positive (x>0.

4. Calculate key points:

• If y=−1 x=2(−1)=0.5

• If y=0 x=2=1

• If y=1 x=2=2

• If y=2 x=2=4

5. Determine the asymptote and intercept. The graph has a vertical asymptote at x=0 and an x-intercept at (1,0)

6. Plot the points (0.5,−1) (1,0) (2,1) and (4,2) and draw a smooth curve through them, extending upwards to the right and downwards towards the y-axis.

Final Answer

(log_2)(x)=y⇒x=2

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