Final answer:
To solve the equation using the change of base formula, rewrite both sides of the equation using the same base. Equate the exponents of the same base and solve for x using logarithmic properties.
Step-by-step explanation:
To solve the equation using the change of base formula, we need to rewrite both sides of the equation using the same base. Let's rewrite 5^(2x-4) using a base of 3:
5^(2x-4) = (3^log3(5))^(2x-4)
Similarly, let's rewrite 3^(x+2) using a base of 3:
3^(x+2) = (3^log3(3))^(x+2) = 3^(x+2)
Now we can equate the two expressions:
(3^log3(5))^(2x-4) = 3^(x+2)
Since the bases are equal, we can equate the exponents:
log3(5) * (2x-4) = x+2
Solving for x, we can use logarithmic properties to simplify the equation:
2log3(5)x - 4log3(5) = x + 2
2log3(5)x - x = 4log3(5) + 2
x(2log3(5) - 1) = 4log3(5) + 2
x = (4log3(5) + 2) / (2log3(5) - 1)