How do you simplify \log _ { 8} ( \root[ 3] { \frac { x ^ { 8} } { y ^ { 7} } } )?

1 Answer
Jan 9, 2018

1/3 (8 log_8 x - 7 log_8 y)

Explanation:

Using the fact that log(u^v) = v log (u) and log(u/v) = log(u)-log(v), we get:

log_8 ( root(3)(x^8 / y^7)) = 1/3 log_8 (x^8/y^7) =
1/3 (log_8 x^8 - log_8 y^7) = 1/3 (8 log_8 x - 7 log_8 y)