To solve this equation, we can first simplify the left side by factoring out a common factor of 3^(x-2):
3^(x+1) - 43^(x-2) = 633^x - 43^x = 6(3-4)3^x = 6-3*3^x = 6-3^x = 69/-3^x = 23
Now, we can rewrite -3^x as 1/(-3^x) and rewrite 23 as 3^2:
1/3^x = 3^2
To solve for x, we can rewrite both sides with the same base:
3^(-x) = 3^2
Since the bases are the same, we can set the exponents equal to each other:
-x = 2
Therefore, the solution to the equation is x = -2.
To solve this equation, we can first simplify the left side by factoring out a common factor of 3^(x-2):
3^(x+1) - 43^(x-2) = 6
33^x - 43^x = 6
(3-4)3^x = 6
-3*3^x = 6
-3^x = 69/
-3^x = 23
Now, we can rewrite -3^x as 1/(-3^x) and rewrite 23 as 3^2:
1/3^x = 3^2
To solve for x, we can rewrite both sides with the same base:
3^(-x) = 3^2
Since the bases are the same, we can set the exponents equal to each other:
-x = 2
Therefore, the solution to the equation is x = -2.