Find a solution to the equation if possible. Give the answer in exact form and in decimal form.

8=4sin(5x)

To solve the equation 8 = 4sin(5x), we need to isolate the variable x. Follow these steps:

Step 1: Divide both sides of the equation by 4 to get sin(5x) alone:
8/4 = sin(5x)
2 = sin(5x)

Step 2: In order to solve for x, we need to find the inverse of the sine function. The inverse of sin is arcsin (also written as asin or sin^(-1)).

Step 3: Apply the inverse sine function to both sides of the equation:
arcsin(2) = arcsin(sin(5x))

Step 4: Use the properties of arcsin to simplify the expression:
arcsin(2) = 5x

Step 5: Divide both sides by 5 to solve for x:
x = arcsin(2) / 5

The solution to the equation 8 = 4sin(5x) is x = arcsin(2) / 5.

To obtain a decimal approximation of the solution, you can use a calculator to find the value of arcsin(2). In decimal form, the solution will be x ≈ 0.4115.