Final answer:
To solve the given equation, rewrite both sides with a common base using the property of exponents. Then, equate the exponents and solve for x.
Step-by-step explanation:
To rewrite the given equation with a common base, we need to express both sides using the same base. In this case, we can rewrite 9^(x+1) as (3^2)^(x+1), and we can rewrite 27^x as (3^3)^x. Next, we can use the property of exponents which states that (a^m)^n is equal to a^(m * n). So, applying this property, we can rewrite the equation as 3^(2*(x+1)) = 3^(3*x).
Now that both sides have the same base, we can equate the exponents. Therefore, 2*(x+1) = 3*x. Simplifying this equation, we get 2x + 2 = 3x. Subtracting 2x from both sides, we get 2 = x.
Therefore, x = 2 is the solution to the equation 9^(x+1) = 27^x.