I want to know how to compare in root. Express large and small. A = 3^(1/3), B = 4^(1/4), C = 6^(1/6) ?

Express large and small.
A = 3^(1/3), B = 4^(1/4), C = 6^(1/6)

1 Answer
Aug 9, 2018

A> B > C

Explanation:

Just take the logarithm (to the base e or 10)

In the given case let us take logarithm to the base10

logA=1/3log3=1/3xx0.4771~=0.1590

logB=1/4log4=1/4xx0.6021~=0.1505

logC=1/6log6=1/6xx0.7781~=0.1297

As logA>logB>logC, we have

A> B > C

This is as logx function is continuously increasing function, as seen from the following graph; as also derivative of logx is 1/x, which is negative only for x<0, which is not in the domain.

graph{logx [-0.29, 9.71, -2.22, 2.78]}