What is the value that satisfies the equation? Note: All necessary steps must be shown on your submitted work in order to earn credit.
27^2x=9^x+4
(1 point)
To solve the equation, we can start by rewriting the exponential terms using the same base:
(3^3)^2x = (3^2)^x+4
Using the property of exponentiation (a^(b*c) = (a^b)^c), we can simplify further:
3^(2*3x) = 3^(2x + 4)
Now, since the bases are the same, we can equate the exponents:
2*3x = 2x + 4
Simplifying the equation:
6x = 2x + 4
Subtracting 2x from both sides:
4x = 4
Dividing both sides by 4:
x = 1
Therefore, the value that satisfies the equation is x = 1.