The figure above represent the graph of [tex]log_{2}(x) [/tex]
We are to approximate the value of y from the equation:
[tex]2^{2y}=3 [/tex]
Taking log to the base 2 of both sides, we get:
[tex]log_{2}(2^{2y})=log_{2}(3) \\ \\
2y(log_{2}(2)= log_{2}(3) \\ \\
2y=log_{2}(3) \\ \\
y= \frac{log_{2}(3)}{2} [/tex]
In order to find the value of y, we first need to find the value of [tex]log_{2}=3 [/tex] from the graph. From the graph we can see that the value of log_{2}(3) is about 1.6, as shown in image attached with.
So,
y = 1.6/2 = 0.8
Thus value of y, as calculated using the graph is 0.8
