Question 64195
This is a tricky log problem.  The best thing to do with logs is to actually raise both sides to a power.  This eliminates the log part of the equation.

If you raise both sides to a power of logx = 5, for example you would get x = 10^5.  

So for your problem, you would raise both sides by the power of 27. 

log27^x=4/3 becomes
27 ^ ( log 27^x ) = 27 ^ ( 4/3) (read 27 to the 4/3 power)

Keep in mind that 27 is 3 cubed.  That's 3 to the 3 power.
( 3 * 4 / 3 ) The quantity 3 times 4 /3 = 4.
so the right side above, copied below is 

{{{27 ^ (4/3) }}} = {{{3 ^ (3 * 4 / 3) }}} = {{{3^4}}} (because the 3's cancel in the exponent part of the equation (the upper)

What is {{{ 3 ^ 4 }}} ?
3 times 3 times 3 times 3
Answer is 27 * 3.
or 81.