Given "$x = \log 8$", it is very easy to rewrite the expression as "$10^x = 8$", which cannot easily be solved for by hand. However, if I plug "$x = \log 8$" into my calculator, I get "$x = 0.903089986992$".
So How Does It Know?
Is there some sort of logarithmic formula implemented by calculators, or does it really just brute-force the value for all of those decimal places?
Note:
I develop apps as a hobby, so if said formula involves loops or binary-operators, don't feel overly pressured to explain how they work; I already understand them.
1 Answer
As pointed out in the comments, it probably uses the Taylor Series, which gives us $$ \ln(1+x)=\sum_{n=1}^\infty \frac{(-1)^{n+1}}{n} x^n = x - \frac{x^2}{2} + \frac{x^3}{3} - \cdots $$ However, more insightful answers are given here.
