How do you evaluate # ln1.4#?

1 Answer
Jul 8, 2016

Answer:

Use a calculator or Taylor series to find:

#ln(1.4) ~~ 0.3364722#

Explanation:

My calculator tells me that:

#ln(1.4) ~~ 0.33647223662121293050#

but can we calculate it without a #ln# function?

We can use the Taylor series:

#ln(1+x) = sum_(n=1)^oo (-1)^(n-1) x^n/n#

So:

#ln(1.4) = ln(1+0.4)#

#= 0.4-0.4^2/2+0.4^3/3-0.4^4/4+...#

#~~0.4-0.08+0.02133333-0.0064+0.002048-0.00068267+0.00023406-0.00008192+0.00002913-0.00001049+0.00000381-0.00000140+0.00000052-0.00000019+0.00000007-0.00000003+0.00000001 = 0.33647223#