Answer
7 terms
Work Step by Step
The Taylor series for $\ln (1+x)$ can be defined as: $\ln (1+x)=x-\dfrac{ x^2}{2}+\dfrac{x^3}{3}-....$ ; $-1 \leq x \leq 1$ and $\ln (1-x)=-x-\dfrac{ x^2}{2}-\dfrac{x^3}{3}-....$ ; $-1 \leq x \leq 1$
We have $| Error|=|\dfrac{(-1)^n x^n}{n}|$
When $ x=0.1$, then we have
$| Error|=|\dfrac{(-1)^n x^n}{n}|=\dfrac{1}{n (10^n)}$
But $\dfrac{1}{n (10^n)} \lt \dfrac{1}{10^8} \implies n \geq 8$
So, we have to consider $7$ terms for the accuracy.
