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 find the value that satisfies the equation 27^(2x) = 9^(x+4), we can rewrite both sides of the equation using the same base.
Since 27 = 3^3 and 9 = 3^2, we have:
(3^3)^(2x) = (3^2)^(x+4)
Using the property of exponents, applying the power of a power rule, we can simplify the equation:
3^(3*(2x)) = 3^(2*(x+4))
We can equate the exponents now:
3*(2x) = 2*(x+4)
Simplifying the equation:
6x = 2x + 8
Subtracting 2x from both sides:
6x - 2x = 2x - 2x + 8
4x = 8
Dividing by 4 on both sides:
4x/4 = 8/4
x = 2
The value that satisfies the equation is x = 2.