Question 6186
1. logbase8 8 = is it 1?  This is correct.
2. logbase3(1/9) = -2??  This is correct
The first two problems seemed to be no problem for you, you simply put them into the same form and solved, so we can rewrite the following problems in the same form to see the answers as well:

3. logbase1/3 9= 27???  rewrite 9 as (1/3)^-2 so the problem is now:
{{{log (1/3)^(1/3)^-2= -2}}} 
4. logbase5 cuberoot25 = rewrite cube root of 25 as {{{5^(2/3)}}} so the problem now reads:
{{{log(5)^5^(2/3)=2/3}}}
5. logbasesqrt3 9 = rewrite 9 as {{{sqrt(3)^4}}}
{{{log (sqrt(3))^(sqrt(3)^4)=4}}}
6. lne^3=  = rewrite this as 3*lne (the lne=1) so, 3*1=3