To solve this equation, we can first simplify the right side of the equation:
(1/2)^x (16/17)^x = (3/2)^(1/2)^x (16/17)^x = 27/8
Now, we can rewrite the left side of the equation as a single base:
(1/2)^(x) (16/17)^x = (1/2 16/17)^= (8/17)^x = 27/8
Now, we can rewrite both sides of the equation with the same base:
(8/17)^x = 27/8/17 = (27/8)^(1/x)
To simplify further, we can take the reciprocal of both sides:
17/8 = (8/27)^x
Now, we can rewrite this in terms of powers of 2 and 3:
17/8 = (2^3 / 3^3)^17/8 = (2/3)^3x
Now, we can compare the corresponding sides:
17/8 = 2/173 = 851 = 16 (False)
Therefore, the equation has no solution.
To solve this equation, we can first simplify the right side of the equation:
(1/2)^x (16/17)^x = (3/2)^
(1/2)^x (16/17)^x = 27/8
Now, we can rewrite the left side of the equation as a single base:
(1/2)^(x) (16/17)^x = (1/2 16/17)^
= (8/17)^x = 27/8
Now, we can rewrite both sides of the equation with the same base:
(8/17)^x = 27/
8/17 = (27/8)^(1/x)
To simplify further, we can take the reciprocal of both sides:
17/8 = (8/27)^x
Now, we can rewrite this in terms of powers of 2 and 3:
17/8 = (2^3 / 3^3)^
17/8 = (2/3)^3x
Now, we can compare the corresponding sides:
17/8 = 2/
173 = 8
51 = 16 (False)
Therefore, the equation has no solution.