Using the graph of f(x) = log₂x below, approximate the value of y in the equation 2^2y = 5.
Log base2 graph

Solution:

Given: 2^2y = 5

Now apply base 2 logarithm on both sides

2y\(\log_2(2)\) = \(\log_2(5)\)

Since \(\log_2(2)\) = 1, we have

2y = \(\log_2(5)\)

y = [\(\log_2(5)\)]/2

From the graph

When x = 5, the approximate value of \(\log_2(5)\) is 2.3

y = [\(\log_2(5)\)]/2 = 2.3/2 = 1.15

Therefore, the approximate value of y is 1.15.

Using the graph of f(x) = log2x below, approximate the value of y in the equation 2^2y = 5.

Summary:

Using the graph of f(x) = log2x below, approximate the value of y in the equation 2^2y = 5 is 1.15.