# F( x ; b) = log_b(x+1/log_b(x+1/log_b(x+...))), x>=b>1.How do you approximate F(15, 10)=1.19958, nearly?

Aug 3, 2016

Contribution

#### Explanation:

From

$y = {\log}_{b} \left(x + \frac{1}{y}\right)$ and calling $b = z$ the surface

$G \left(x , y , z\right) = {z}^{y} - x - \frac{1}{y} = 0$ for

( (-5 < x < 5), (-5 < y < 5), (0< z < 5))

locally, has the aspect below