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Question

If x changes from 4 to 4.01 then find the approximate change in log x.

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Solution

Given,
x=4

On taking log both sides, we get
log x=log 4 ...... (1)

Now,
x+δx=4.01
On taking log both sides, we get
log (x+δx)=log 4.01 ......(2)

Divide both equations such that equation(2)equation(1), we get
log(x+δx)log x=log(4.01)log 4

log(x+δxx)=log(4.014) [from the properties of log]
log(x+δxx)=log(0.01)
log δx=log(10)2
log δx=2log10
=2×1=2.

Hence, this is the answer.

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