Question

Which of the following graphs is the same as y = log1/2x? x = 2y x = 2-y x = -(2y)

Answer 1

We can convert the logarithmic equation to exponential equation to find its equivalent equation.

$y= log_{ \frac{1}{2} }(x)$

Shifting the base of log(1/2) to the other side of the equation, we can write:

$(\frac{1}{2})^{y} =x \\ \\ x= \frac{ 1^{y} }{ 2^{y} } \\ \\ x= \frac{1}{ 2^{y} } \\ \\ x= 2^{-y}$