log a (x)
log a ( x ^ ( 1 / b ) ) = ---------
b
The derivation of this law is identical to the derivation of Logarithm Law 5
For example, we can show that log 2 ( 5√ 7) = log 2 (7) / 5.
log 2 ( 5√ 7) = log 2 ( 7 ^( 1/5 ) )
= 1/5 log 2 (7)
= log 2 (7) / 5
Therefore, log 2 ( 5√ 7) = log 2 (7) / 5
1. log 2 (4√ 8) = log 2 ( 8 ^ (1/4) )
= 1/4 log 2 (8)
= 1/4 log 2 ( (2)^3 )
= 3/4 log 2 (2)
= 3/4
2. log 8 (10√10) = log 8 (10 ^ (1/10))
= 1/10 log 8 (10)
3. log 16 (y√ x) = log 16 (x ^ (1/y))
= 1/y log 16 (x)
4. log z ( x√ y) = log z (y ^ (1/x))
= 1/x log z (y)
5. log x ( 2x √ y) = log x (y ^ (1/2x))
= 1/2x log x (y)
