Graph log base a of x

Problem

y=(log_a)(x)

Solution

1. Identify the domain and range of the logarithmic function. The domain is x>0 and the range is all real numbers.

2. Determine the vertical asymptote. The graph approaches the y-axis as x approaches 0 from the right, so the vertical asymptote is x=0

3. Plot the x-intercept. Since (log_a)(1)=0 for any base a>0 and a≠1 the graph always passes through the point (1,0)

4. Identify a reference point. Since (log_a)(a)=1 the graph passes through the point (a,1)

5. Consider the base a If a>1 the function is increasing (growth). If 0<a<1 the function is decreasing (decay).

6. Sketch a smooth curve starting near the vertical asymptote x=0 passing through (1,0) and (a,1) and continuing to the right.

Final Answer

y=(log_a)(x)

Want more problems? Check here!