math - Multiply a number by a ratio n times to achieve a desired number -

math - Multiply a number by a ratio n times to achieve a desired number -

i'm trying scale image downwards in steps avoid artifacts. have 800 square pixel image needs scaled downwards 100 square pixels. want perform scaling in variable number of iterations. lets want go 800 100 in 3 iterations. how find ratio apply image each time accomplish desired size?

if want accomplish final ratio r, in n steps, ratio @ each step n-th root of r, or equivalently, r^(1/n). example, r=1/8, , n=3, ratio @ each step (1/8)^(1/3), or 1/2.

math logarithm exponent