SOLUTION: Consider the equation: 5^(2x-1)=3^(x+4) Use the properties of logarithms to rewrite your exact solution in the form log(b)a

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Consider the equation: 5^(2x-1)=3^(x+4) Use the properties of logarithms to rewrite your exact solution in the form log(b)a      Log On


   

Question 592237: Consider the equation: 5^(2x-1)=3^(x+4)
Use the properties of logarithms to rewrite your exact solution in the form log(b)a
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
52x-1 = 3x+4

log(52x-1) = log(3x+4)

(2x-1)log(5) = (x+4)log(3)

Let log(5) = A
Let log(3) = B

     (2x-1)A = (x+4)B

     A(2x-1) = B(x+4)

     2Ax - A = Bx + 4B

    2Ax - Bx = A + 4B

   x(2A - B) = A + 4B

           x = %28A%2B4B%29%2F%282A-B%29

           x = %28log%28%285%29%29%2B4log%28%283%29%29%29%2F%282log%28%285%29%29-log%28%283%29%29%29

You can leave it like that or write it as the quotient of two logs:

           x = %28log%28%285%29%29%2Blog%28%283%5E4%29%29%29%2F%28log%28%285%5E2%29%29-log%28%283%29%29%29
           
           x = %28log%28%285%29%29%2Blog%28%2881%29%29%29%2F%28log%28%2825%29%29-log%28%283%29%29%29

           x = log%28%285%2A81%29%29%2Flog%28%2825%2F3%29%29

           x = log%28%28405%29%29%2Flog%28%2825%2F3%29%29

Edwin