Homework Help: math

Posted by APPRECIATIVE STUDENT on Wednesday, January 19, 2011 at 8:57am.

Thank you for your help.
I don't know how to do this, so if you could explain step by step how to do this, that would be really good....
"A rough approximation for ln(5) is 1.609. Use this apporximation and differentials to approximate ln(521/100)

thanks

math - Reiny, Wednesday, January 19, 2011 at 12:03pm
let y = ln(x)
x = 5

dy/dx = 1/x
dy = (1/x)dx

dx = 521/100 - 5 = .21 , y = ln(5) = 1.609

dy = (1/5)(.21) = .042

ln(521/100)
= ln (5.21) = appr. y + dy
= 1.609 + .042 = 1.651

check: ln(5.21) = 1.6505 (by calculator)
not bad

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