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I have gotten as far as 3^3(4z)=3^2(z+1)

log both sides

27^4z=9^(z+1)
log(27^4z) = log(9^(z+1))
4z (log(27)) = (z+1) (log(9))
get like terms together now

you can "remember" exponents if you want and try to recall what is what... but it is harder

4z (log(27)) = (z+1) (log(9))
4z.3log (3)= (z+1)2log (3)
12z=2z+2
z=1/5

the relation is this:
B^x = y
x = logB(y)

3^2 = 9
2 = log3(9)

THAT is what I needed :D The exponent rule.

I got it right easily that time. Just didn't know what to do with it, thank you very much d:D

:)

easy when you can "know" the base..