The positive value of x that satisfies the equation (3 + 2x)^5 = (1 + 3x)^4 is between
Bunuel, can you please explain this one? Choose the most appropriate option.
A) 0 and 0.5 B) 0.5 and 1 C) 1 and 1.5 D) 1.5 and 2 E) 2 and 2.5

Rationale: trial and error would probably be the easiest way to solve this problem . when x is large enough positive number , then because of the exponents ( 5 > 4 ) , lhs will be more than rhs ( as you increase the positive value of x the distance between the values of lhs and rhs will increase ) . try x = 1 - - > lhs = 3 ^ 5 = 81 * 3 = 243 and rhs = 4 ^ 4 = 64 * 4 = 256 , so ( 1 + 2 x ) ^ 5 < ( 1 + 3 x ) ^ 4 . as you can see lhs is still slightly less than than rhs . so , the value of x for which ( 1 + 2 x ) ^ 5 = ( 1 + 3 x ) ^ 4 is slightly more than 1 . answer : d .
Answer: D