SOLUTION: 25*125^2r = 25^3r+3 Please show steps and solution

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


   

Question 1135951: 25*125^2r = 25^3r+3 Please show steps and solution
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

25%2A125%5E%282r%29+=+25%5E%283r%29%2B3............since 125%5E%282r%29+=25%5E%283r%29, we have

25%2A25%5E%283r%29=+25%5E%283r%29%2B3

25%2A25%5E%283r%29-+25%5E%283r%29=3

24%2A25%5E%283r%29=3

25%5E%283r%29=3%2F24

25%5E%283r%29=1%2F8........take log of both sides

log%2825%5E%283r%29%29=log%281%2F8%29

%283r%29log%2825%29=log%281%29-log%288%29......log%281%29=0

%283r%29log%285%5E2%29=-log%282%5E3%29

%283r%29%2A2log%285%29=-3%2Alog%282%29

r=-%28cross%283%29%2Alog%282%29%29%2F%28cross%283%29%2A2log%285%29%29

r=-%28log%282%29%29%2F%282log%285%29%29





Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
25*125^2r = 25^3r+3 Please show steps and solution
If matrix%281%2C3%2C+25%28125%29%5E%282r%29%2C+%22=%22%2C+25%5E%283r+%2B+3%29%29, then:



matrix%281%2C3%2C+%285%5E2%29%285%29%5E%286r%29%2C+%22=%22%2C+5%5E%286r+%2B+6%29%29

matrix%281%2C3%2C+5%5E%282+%2B+6r%29%2C+%22=%22%2C+5%5E%286r+%2B+6%29%29

2 + 6r = 6r + 6 ------- Bases are equal and so are their exponents

6r - 6r = 6 - 2

0+%3C%3E+4, so NO SOLUTIONS. <======= CORRECT ANSWER, considering the correct equation was solved



You DON'T NEED LOGS or any complex calculations to solve this equation....just the laws of exponents! 

Using logs is just a waste of time and effort, unless you're requested to use logs, of course.