Simplify log3(1/27)^4
Would this simplify down to
4 log3^1 - 4log3^3

Question

tkhunny · Answer

??  The "3" is a Base, not an argument.

$1/27 = 3^{-3}$

anonymous · Answer

4 log3 1 - 4 log3 3^(-3)

tkhunny · Answer

You missed the first hint.  $\log_{3}(a)$ has only a little to do with $\log(3)$

$\log_{3}(1/27)^{4} = 4\cdot\log_{3}(1/27) = 4\cdot\log_{3}(3^{-3}) = -12\cdot\log_{3}(3)$

Can you finish?  Only one more thing to do.

anonymous · Answer

What do I need to do to finish? 
4 log3 1 - (-12 log3 (3)?

hartnn · Answer

use the fact that log 1 in any base = 0
and  $\log_aa=1$
so, $\log_33=1$

hartnn · Answer

how did you get 2 negatives ?

hartnn · Answer

27 is $3^3$ 
and not $3^{-3}$

anonymous · Answer

Ok so am I looking at 4 log3  1-12 or have I gotten my self so confused I' way off ?

hartnn · Answer

so you used $\log_33=1$
and thats correct!
now also use the fact that 
$\log_31=0$

anonymous · Answer

So  my answer is 0-12 ?

hartnn · Answer

which is -12 and yes :)

anonymous · Answer

Finally!!!! Thank you ever so much!

hartnn · Answer

you're most welcome ^_^