SOLUTION: Hi, I'm having difficulty solving this equation. 5^(3a)*4^(2a+1)-10^(3a+2)=0 (expressing the answer in the form (lnx)/(lny) Thanks

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hi, I'm having difficulty solving this equation. 5^(3a)*4^(2a+1)-10^(3a+2)=0 (expressing the answer in the form (lnx)/(lny) Thanks       Log On


   

Question 596644: Hi, I'm having difficulty solving this equation.
5^(3a)*4^(2a+1)-10^(3a+2)=0
(expressing the answer in the form (lnx)/(lny)
Thanks
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
5^(3a) * 4 * 4^(2a) = 100 * 10^(3a)

(3a)ln(5) + ln(4) + (2a)ln(4) = ln(100) + (3a)ln(10)

(3a)ln(5) + (2a)ln(4) - (3a)ln(10) = ln(100) - ln(4)

a[ln(5^3 * 4^2 / 10^3)] = ln(100 / 4)

a = [ln(25)] / [ln(2)]