log r - log r^3 - log r^5 =8√2 , if all the logarithms are in base 2, find r.

1 answer

Using the properties of logarithms, we can simplify the equation as follows:

log r - log r^3 - log r^5 = 8√2

log r - 3log r - 5log r = 8√2

-7log r = 8√2

log r = -8√2 / 7

Since the logarithms are in base 2, we can rewrite the equation as:

r = 2^(-8√2 / 7)

Therefore, r ≈ 0.7027.