Question

Using the graph of f(x) = log2x below, approximate the value of y in the equation 2^(2y) = 3.

Answer 1

The figure above represent the graph of $log_{2}(x)$

We are to approximate the value of y from the equation:

$2^{2y}=3$

Taking log to the base 2 of both sides, we get:

$log_{2}(2^{2y})=log_{2}(3) \\ \\ 2y(log_{2}(2)= log_{2}(3) \\ \\ 2y=log_{2}(3) \\ \\ y= \frac{log_{2}(3)}{2}$

In order to find the value of y, we first need to find the value of $log_{2}=3$ 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