Question

If logₑ4=1.3868, then approximate value of logₑ4.01 =.......,Select correct option from the given options.
(a) 1.3867
(b) 1.3869
(c) 1.3879
(d) 1.3893

Answer 1

answer : option (d) 1.3893

explanation : here, logₑ4 = 1.3868

let ,y = logₑx [ where x = 4, and y = 1.3868]

differentiating y with respect to x,

dy/dx = 1/x

using , ∆y = (dy/dx)∆x

or, ∆y = (1/x) ∆x......(1)

now, f(x + ∆x) = logₑ(x + ∆x) [ here, ∆x = 0.01 ]

we know, ∆y = f(x + ∆x) - f(x)

so, ∆y = logₑ(x + ∆x) - logₑx

from equation (1),

∆y = (1/4) × 0.01 = 0.01/4 = 0.0025

now, ∆y + logₑx = logₑ(x + ∆x)

or, 0.0025 + logₑ4 = logₑ(4.01)

or, 0.0025 + 1.3868 = logₑ(4.01)

or, logₑ(4.01) = 1.3893

hence, option (d) is correct choice.