find the approximate values of log10(4.04), it being given that log104 = 0.6021 and log10e = 0.4343

Q9 of 292 Page 469

find the approximate values of log₁₀(4.04), it being given that log₁₀4 = 0.6021 and log₁₀e = 0.4343

Let

∴

Let x =4 and Δx = 0.04.

⇒

We, know

⇒

∴

⇒

∴ Δy = 0.004343

Also,

Δy = f(x+Δx)-f(x)

∴ 0.004343 = log_e(4+0.04) – log_e(4)

⇒ 0.004343 = log_e(4.04) – 0.6021

⇒ log_e(4.04) = 0.606443.

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