By writing x as 4+(x-4) and using the Maclaurin expansion for ln(1+t), or otherwise, find the first four non zero terms in the Taylor series expansion for
ln(5x)

about x = 4.

Question

By writing x as 4+(x-4) and using the Maclaurin expansion for ln(1+t), or otherwise, find the first four non zero terms in the Taylor series expansion for 
ln(5x) 
 
about x = 4.

jamesj · Answer

ln(5x) = ln 5 + ln x
          = ln 5 + ln(4 + (x-4))
          = ln 5 + ln 4 + ln(1 + (x-4)/4)
          = ln(20) + ln(1 + u), where u = (x-4)/4

Now use the series expansion for ln(1+u)