# Taylor Expansion and Log transformation (Time Series)

From: Time Series Analysis with Applications in R by Jonathan D. Cryer and Kung-Sik Chan.

Here is the Taylor expansion: $\log Y_t = \sum_{n = 1}^{\infty} (-1)^{n+1} \frac{(Y_t - 1)^n}{n}$. How come there is $\mu_t$ in the equation with the red question mark? I don't see a way to derive it.

Hint: By Taylor expansion, we have $f(x) \approx f(a)+(x-a)f'(a)$ near $a$. Now let $f(x)=\log x, a=\mu_t$ and $x=Y_t$.