Find the logarithm log{2/3] (8/27)

Question

anonymous · Answer

$$\log_{2/3} 8/27$$ 
Log to the base 2/3 of 8/27

anonymous · Answer

So we can re-write this as an exponent$$2/3^x = 8/27$$.
Or$$2^x/3^x$$    

So, this question is asking log(2/3) (8/27),  or what power do we have to raise 2/3 by to get 8/27.

Conveniently, 2^3 =8, and 3^3=27, so (2/3)^3 = 8/27.

So the log(2/3) (8/27) =3

Hope this helps.

anonymous · Answer

Sorry, couldn't get that equation writing to work.

directrix · Answer

Let  log{2/3] (8/27) = x.

By definition of logarithms, then

(2/3) ^ x  =  8/27            @Ratedover    Do you agree so far?

directrix · Answer

(2/3) ^ x  =  8/27

(2/3) ^ x   =  ( 2 / 3 ) ^ 3

x = ? 

@Ratedover