Another approach: Let y=2^x Then, (8^x + 64^x)÷((16^x + 32^x)= 3÷2 can be simplified as (y^3 + y^6)÷(y^4 + y^5) = 3÷2 Cross-multiplying and simplifying gives 2y^6 - 3y^5 - 3y^4 + 2y^3 = 0 Because y≠0 we can divide the above eqn by y^3 to get 2y^3 - 3y^2 -3y +2 = 0 Factoring the above eqn gives, (2y -1)(y +1)(y - 2) = 0 Thus, y = 1/2 or y = -1 or y = 2 Because y = 2^x can never be negative y = -1 is an extraneous solution and is discarded. Therefore, 2^x = 1/2 or 2^x = 2 Solving for x is the same as you showed. x = -1 or x = 1
Please! Prior to each step you really should explain what you are about to do and the reason why! This approach is not very instructive. All you are doing is showboating!
Another approach:
Let y=2^x
Then, (8^x + 64^x)÷((16^x + 32^x)= 3÷2 can be simplified as
(y^3 + y^6)÷(y^4 + y^5) = 3÷2
Cross-multiplying and simplifying gives
2y^6 - 3y^5 - 3y^4 + 2y^3 = 0
Because y≠0 we can divide the above eqn by y^3 to get
2y^3 - 3y^2 -3y +2 = 0
Factoring the above eqn gives,
(2y -1)(y +1)(y - 2) = 0
Thus,
y = 1/2 or y = -1 or y = 2
Because y = 2^x can never be negative y = -1 is an extraneous solution and is discarded.
Therefore,
2^x = 1/2 or 2^x = 2
Solving for x is the same as you showed.
x = -1 or x = 1
Other option is to reduce all the terms to multiples of 2. This will simplify his calculations
X = 1
No need for two variables a&b
Please! Prior to each step you really should explain what you are about to do and the reason why! This approach is not very instructive. All you are doing is showboating!
ху=й