Since solving this equation machanically is not the fastest way, so you might want to plug numbers in.

For zero, clearly it satisfies the equation, so keep it. Then lol we are done. All the other options don’t contain 0 is wrong.

Edit:

all the solutions to this equation

I’m guessing ‘the positive value of x that satisfies the equation is **between**’ means that *0 and 0.5* both aren’t inclusive

Is that the case? @pratik3818

Actually,this is a flawed question, the only solution to this equation is zero.

Cite the source maybe? @pratik3818

Yes , 0 does not work, cause it’s not a positive integer

Yes true

A little bit of plugging in:

when x = 0.5, (1 + 2x)^5 = 32 and (1 + 3x)^4 = 2.5^4 = 39.0625.

when x = 1, (1 + 2x)^5 = 243 and (1 + 3x)^4 = 4^4 = 256.

when x = 1.5, (1 + 2x)^5 = 1024 and (1 + 3x)^4 = 5.5^4 ~ 915.

So notice that between x = 1 and x = 1.5, the LHS becomes bigger than the RHS, but till then it was the other way round. Given that both the LHS and RHS are purely monotonic, this means that there is a point between 1 and 1.5 where the LHS and RHS are equal. Hence the answer is C.