Question 7040
1. {{{log(x^2-9)-log(x+3)=3}}} base4 is assumed.

{{{log((x^2-9)/(x+3)) = 3}}}
{{{((x+3)(x-3)/(x+3)) = 4^3}}}
{{{((x+3)(x-3)/(x+3)) = 64}}}
{{{(x-3) = 64}}}
--> x=67


2. logbase9 x + 3 logbase3 x = 14. I will convert the base9 to base3 and then everything will be base3.


{{{logx/log9 + 3log(x) = 14}}}
{{{logx/2 + 3log(x) = 14}}}
{{{logx + 6log(x) = 28}}}
{{{logx + log(x^6) = 28}}}
{{{log(x*x^6) = 28}}}
{{{log(x^7) = 28}}}
{{{(x^7) = 3^28}}}
 --> {{{x = (3^28)^(1/7)}}}
 --> {{{x = 3^4}}}
 --> x = 81


jon.