To solve for x in the equation log(16x) = 3/2, we need to use the definition of logarithms, which states that log base b of a is equal to c if and only if b raised to the power of c equals a.
In this case, we have:
log(16x) = 3/2
Rewriting this in exponential form, we get:
10^(3/2) = 16x
We can simplify 10^(3/2) as follows:
10^(3/2) = 10^(1/2) * 10^1 * 10^(1/2) = (sqrt(10))^2 * 10^(1/2) = 10 * sqrt(10)
Therefore, we have:
16x = 10 * sqrt(10)
Dividing both sides by 16, we get:
x = (10 * sqrt(10)) / 16
Simplifying this expression, we get:
x = (5 * sqrt(10)) / 8
So the solution to the equation log(16x) = 3/2 is x = (5 * sqrt(10)) / 8.