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Chapter 4: Q. 73 (page 401)

Prove that lnxis zero if x=1, negative if 0<x<1, and positive if x>1.

Short Answer

Expert verified

lnxis zero if x=1, negative if 0<x<1, and positive if x>1.

Step by step solution

01

Step 1. Given information

We have to prove that lnxis zero if x=1, negative if 0<x<1, and positive if x>1.

02

Step 2. Proof of the question.

lnxcan be written as 鈭�1x1tdt

Forx=1,

ln1=鈭�111tdt=0

For 0<x<1,

lnx=鈭�1x1tdt=-鈭�x11tdt

So, lnxis negative.

Now for x>1,

lnx=鈭�1x1tdt

So,lnxis positive.

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