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

1 Answer
Prof_S
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)#

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