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Question

y=logx satisfies for x>1, the equality

A
x1>y
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B
x21>y
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C
y>x1
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D
x1x<y
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Solution

The correct options are
A x1>y
B x21>y
D x1x<y
Consider f(x)=logx(x1)f(x)=1x1
So f(x)<0 for x>1.
Thus f(1)>f(x) for x>1
0>logx(x1)x1>logx

Consider g(x)=x1xlogxg(x)=(x12)2+14x2>0
for all x.
Hence g(x)>g(1),x>1x1x>logx

x21>logx is true (we can check by taking x=2)

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