To solve the equation 2^(2y) = 6 log2(x), we can start by isolating y.
First, we can rewrite the equation as:
2y = log2(6 log2(x))
Next, divide both sides by 2:
y = (1/2) * log2(6 log2(x))
Now, to approximate the value of y using the graph of f(x) = log2(x), we need to find the value of log2(x) for a specific x value on the graph.
For example, if we estimate x = 4 from the graph:
- log2(4) = 2
Substituting this into the equation, we find:
y = (1/2) * log2(6 * 2)
Now, calculate:
- 6 * 2 = 12
- log2(12) ≈ 3.585 (approx.)
Substituting back, we have:
y ≈ (1/2) * 3.585 ≈ 1.7925
So, by approximating from the graph and following the calculation, we can conclude that the value of y is approximately 1.79.