Question 139884
(#1) -2logbase3(1/x)+1/3logbase3(squa rt OF x) 

=  -2log3 (x^-1) + (1/3)log3 x^(1/2)

=  (-1)(-2)log3 x  + (1/2)(1/3)log3 x

= 2log3 x  +  (1/6) log3  x

= (13/6)log3 x

-------------------------------------

(#2) 2log2-3logx-1/2[log(x+3)log(x-2)] 

= 2log2 - logx -(1/2)[log(x+3)log(x-2)]

= log(4/x) -(1/2)log(x+3)*log(x-2)

---------------------------------------

express as sum & difference of logarithms, express powers as factors: 
(#3) ln(x^3sqrt[(x^2+1)/(x-3)]

= 3lnx + (1/2)ln[(x^2+1)/(x-3)]

-----------------------------------------

solve each equation: 
(#4) log(7x+8)=2logx 

log(7x+8) = log x^2

7x+8 = x^2
x^2-7x-8 = 0
(x-8)(x+1) = 0
Potitive solution:
x = 8
=============
Cheers,
Stan H.