Write the first 4 terms of the logarithmic series
`log(1+4x)`
Find the intervals on which the expansions are valid.

Write the first 4 terms of the logarithmic series log(1-2x) Find the intervals on which the expansions are valid.

Write the first 4 terms of the logarithmic series log((1-2x)/(1+2x)) Find the intervals on which the expansions are valid.

Write the first 4 terms of the logarithmic series log((1+3x)/(1-3x)) Find the intervals on which the expansions are valid.

Write down the first 3 terms in the expansion of (1+4x)^(-4)

Find the first four terms in the expansion of log(1+tan x) in the power of x.