Respuesta :

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
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