There's a property of logs I want you to remember, that is:
log(a)ᵇ = b*log(a)
We'll be using this property to solve the question
Finding x:
log(2)ˣ = log(3)
x*log(2) = log(3) [using the property mentioned above]
x = log(3) / log(2) [dividing both sides by log(2)]
Hence, the correct answer is option E.