4 5n 113 1 0Solution45n 113 1 0 45n 113 1 5n 113

Solution

4(5n - 1)^1/3 - 1 = 0

==> 4(5n - 1)^1/3 = 1

==> (5n - 1)^1/3 = 1/4

==> (5n -1) = (1/4)³          since a^1/n = b ==> a = bⁿ

==> (5n -1) = 1/64         since (a/b)³ = a³/b³ ; 1³ = 1 , 4³ = 64

==> 5n = 1 + 1/64

==> 5n = 65/64

==> n = 65/(5*64)

==> n = 13/64