solve the equation below. Please show all work. log3(x/2-9)=4
To solve the equation log3(x/2-9) = 4, we need to isolate the variable x.
Step 1: Apply the logarithmic property
By applying the logarithmic property, we rewrite the equation in exponential form:
3^4 = x/2 - 9
Step 2: Simplify the exponent
Simplifying the exponent 3^4, we get:
81 = x/2 - 9
Step 3: Add 9 to both sides
To isolate the x/2 term, we add 9 to both sides of the equation:
81 + 9 = x/2 - 9 + 9
90 = x/2
Step 4: Multiply both sides by 2
To isolate the x, we multiply both sides by 2:
90 * 2 = (x/2) * 2
180 = x
Step 5: Final Answer
Therefore, the solution to the equation log3(x/2-9) = 4 is x = 180.