Final answer:
To solve the equation 9^(2x-2) = 81^(2x-3), we can simplify both sides by using the fact that 81 = 9^2. By equating the exponents, the value of x is found to be 2.
Step-by-step explanation:
To solve the equation 9^(2x-2) = 81^(2x-3), we can simplify both sides by using the fact that 81 = 9^2. Thus, we have:
9^(2x-2) = (9^2)^(2x-3)
Using the property of exponents, we can multiply the exponents:
9^(2x-2) = 9^(4x-6)
Now, by comparing the bases on both sides, we can equate the exponents:
2x-2 = 4x-6
Subtract 2x from both sides:
-2 = 2x-6
Add 6 to both sides:
4 = 2x
Divide both sides by 2:
x = 2