Question

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

Answer 1

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

Answer 2

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.

Answer 3

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

Answer 4

Let log{2/3] (8/27) = x.

By definition of logarithms, then

(2/3) ^ x = 8/27 @Ratedover Do you agree so far?

Answer 5

(2/3) ^ x = 8/27

(2/3) ^ x = ( 2 / 3 ) ^ 3

x = ?

@Ratedover