Difference of Logarithms/Proof 3

Theorem

$\log_b x - \log_b y = \map {\log_b} {\dfrac x y}$

$\ds \map {\log_b} {\frac x y} + \log_b y$

$=$

$\ds \map {\log_b} {\frac x y \times y}$

$\ds $

$=$

$\ds \log_b x$

$\ds \leadsto \ \ $

$\ds \map {\log_b} {\frac x y}$

$=$

$\ds \log_b x - \log_b y$

subtracting $\log_b y$ from both sides

$\blacksquare$

1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.2$: Numbers, Powers, and Logarithms: Exercise $15$