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
Shwetank Mauria
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 base#10#

#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]}

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