Question

For how many positive values of n are both n3 and 3n four-digit integers?

Answer 1

No positive value of n

Explanation:

we have to find out for how many positive values of n are both

`n^3 , 3^n` our-digit integers

Let us consider first cube

we get 4digit lowest number is 1000 and it has cube root as 10.

Thus 10 is the least integer which satisfies four digits for cube.

The highest integer is 9999 and it has cube root as 21.54

or 21 the highest integer.

Considering 3^n we get,

3^10 is having 5 digits and also 3^21

Thus there is no positive value of n which satisfy that both n cube and 3 power n are four digits.