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
To solve the equation 27^(2x) = 9^(x+4), we can rewrite both bases as powers of 3, since 27 = 3^3 and 9 = 3^2:
(3^3)^(2x) = (3^2)^(x+4)
Applying the power of a power rule, we can simplify:
3^(3*2x) = 3^(2*(x+4))
Now, we can equate the exponents:
3^(6x) = 3^(2x+8)
Since the bases are the same, we can set the exponents equal to each other:
6x = 2x + 8
Subtracting 2x from both sides:
4x = 8
Dividing both sides by 4:
x = 2
Therefore, the value x = 2 satisfies the equation 27^(2x) = 9^(x+4).