How do you graph this logarithmic equation by rearranging it y=2log1/2x) the log base is 1/2

Question

Graph the logarithmic function y=2log1/2x . State it's domain and range.

Answer 1

y=2log_½(x), y=-2log₂(x), y=2log₂(1/x) are all equivalent.

To help you plot the graph, we pick values of x which are powers of 2:

  x  y

  ½ 2

  1  0 (x-intercept)

  2 -2

  4 -4

  8 -6

16 -8 (not shown on this graph)

Note that the y-axis is an asymptote and that when x<1 y is positive.