Final answer:
To solve the equation 9^(3x-7) = 9^(5-x), set the exponents equal to each other and solve for x.
Step-by-step explanation:
To solve the equation 9^(3x-7) = 9^(5-x), we can use the property of exponentiation that states when two exponential expressions with the same base are equal, their exponents must be equal as well. In this case, the base is 9. So, we can set the exponents equal to each other:
3x - 7 = 5 - x
Solving for x, we can add x and 7 to both sides:
3x + x = 5 + 7
Combining like terms:
4x = 12
Dividing both sides by 4:
x = 3