Question

Solve the logarithmic function of ln(\(\frac{1+5x}{1+3x}\)).

(a) 2x – 8x^2 + \(\frac{152x^3}{3}\) – …

(b) x^2 + \(\frac{7x^2}{2} – \frac{12x^3}{5}\) + …

(c) x – \(\frac{15x^2}{2} + \frac{163x^3}{4}\) – …

(d) 1 – \(\frac{x^2}{2} + \frac{x^4}{4}\) – …

The question was asked in my homework.

I'd like to ask this question from Discrete Probability topic in chapter Discrete Probability of Discrete Mathematics

Answer 1

The correct option is (a) 2x – 8x^2 + \(\frac{152x^3}{3}\) – …

To explain: To solve the logarithmic function ln(\(\frac{1+5x}{1+3x}\)) = ln(1+5x) – ln(1+3x) = (5x – \(\frac{(5x)^2}{2} + \frac{(5x)^3}{3}\) – …) – (3x – \(\frac{(3x)^2}{2} + \frac{(3x)^3}{3}\) – …) = 2x – 8x^2 + \(\frac{152x^3}{3}\) – …