Solve the equation below. Please show all of your work.

Log3((x/2)-9) = 4

by definition ...

x/2- 9 = 3^4
x - 18 = 162
x = 180

(x/2)-9 = 3^4 = 81

x/2 = 90
x = 180

To solve the equation log3((x/2) - 9) = 4, we need to isolate x.

Step 1: Exponentiate both sides using the base 3.
3^4 = (x/2) - 9

Step 2: Simplify the left side of the equation.
81 = (x/2) - 9

Step 3: Add 9 to both sides.
81 + 9 = (x/2) - 9 + 9
90 = (x/2)

Step 4: Multiply both sides by 2 to isolate x.
2 * 90 = 2 * (x/2)
180 = x

Therefore, the solution to the equation log3((x/2) - 9) = 4 is x = 180.