To solve the given equation:
3^(2x) - 2 3^(2x-1) - 2 3^(2x-2) = 1
We can simplify the equation by factoring out common terms:
3^(2x-2) (3^2 - 2*3 - 2) = 1
Now, evaluate the expression within the parentheses:
3^(2x-2) (9 - 6 - 2) = 13^(2x-2) (1) = 13^(2x-2) = 1
Now, we know that 3^0 = 1. Therefore, we can conclude that:
2x - 2 = 02x = 2x = 1
So, x = 1 is the solution to the given equation.
To solve the given equation:
3^(2x) - 2 3^(2x-1) - 2 3^(2x-2) = 1
We can simplify the equation by factoring out common terms:
3^(2x-2) (3^2 - 2*3 - 2) = 1
Now, evaluate the expression within the parentheses:
3^(2x-2) (9 - 6 - 2) = 1
3^(2x-2) (1) = 1
3^(2x-2) = 1
Now, we know that 3^0 = 1. Therefore, we can conclude that:
2x - 2 = 0
2x = 2
x = 1
So, x = 1 is the solution to the given equation.