SOLUTION: 25*125^2r = 25^(3r+3) Please show steps and explain

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 25*125^2r = 25^(3r+3) Please show steps and explain      Log On


   

Question 1135965: 25*125^2r = 25^(3r+3) Please show steps and explain
Answer by greenestamps(13214) About Me  (Show Source):
You can put this solution on YOUR website!


25%2A125%5E%282r%29+=+25%5E%283r%2B3%29

(1) Usually when an exponent in an equation is of the form ax+b, it is going to help if you separate the expression into two parts. In your example, rewrite "25^(3r+3)" as the product of 25^(3r) and 25^3.
25%2A125%5E%282r%29+=+25%5E3%2A25%5E%283r%29

(2) The bases for the exponents are 125 and 25, which are both powers of 5. So rewrite the equation using 5 as the base for the exponents.
25%2A%285%5E3%29%5E%282r%29+=+25%5E3%2A%285%5E2%29%5E%283r%29

25%2A5%5E%286r%29+=+25%5E3%2A5%5E%286r%29%29

And now we have a problem. 5^(6r) is a positive number, so we can divide both sides of the equation by it to get

25+=+25%5E3

That is clearly false; that means the original equation has no solution.