Question

simplify the expression
2log(4)9-log(2)3
*(base)

i know the answer is log(2)3 but i can't figure out the work to get that answer

Answer 1

Use the rules for changing the base of a logarithm at
http://oakroadsystems.com/math/loglaws.htm#NewBase

It says that
log(a)x = log(b)x/log(b)a

In your case, use it to show that
log(4)9 = log(2)3^2/log(2)4
= 2log(2)3/log(2)4 = log(2)3 !!
Therefore 2log(4)9 = 2 log(2)3
Subtracting 2log(2)3 from that leaves you with log(2)3

Answer 2

The last line should read:
Subtracting log(2)3 from 2log(2)3 leaves you with log(2)3