To approximate the value of y in the equation 2^(2y) = 5 using the graph of f(x) = log2(x), we first need to isolate y. Start by rewriting the equation:
Taking the logarithm base 2 of both sides gives us:
2y = log2(5)
Next, we can solve for y:
y = (1/2) * log2(5)
Now, to find log2(5) using the graph:
- Locate the point on the graph where x = 5.
- Read the corresponding y-value from the graph, which represents log2(5).
Once you have that value, you can substitute it back into the equation for y:
y = (1/2) * (value of log2(5) from the graph).
This will give you the approximate value for y. Be sure to check the scale of your graph for accuracy when reading the value.