Harvard University Admission Question | Solve For x? | Algeria 

We can write 30 as 3^3 +3 right at the beginning to get a =9. Since the function on the left is increasing this is the only point where it cuts the function y=30 and hence this is the only solution

x= log 75/log 45 = (log3+ 2 log5)/(2log 3+log 5) 2x-1= 3log 5/(2log 3+log 5) And x-2 = -3 log3/(2log 3+log 5) hence (2x-1)/(x-2) = - log 5 base 3 or log(1/5) base 3