SOLUTION: Can you show me how to solve e^(5ln3 - 4ln5) using the properties of logarithms? The answer is 243/625, but I want to know step by step how to get there? Thank you!

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Can you show me how to solve e^(5ln3 - 4ln5) using the properties of logarithms? The answer is 243/625, but I want to know step by step how to get there? Thank you!      Log On


   

Question 917571: Can you show me how to solve e^(5ln3 - 4ln5) using the properties of logarithms? The answer is 243/625, but I want to know step by step how to get there? Thank you!
Found 2 solutions by Hawksfan, MathTherapy:
Answer by Hawksfan(61) About Me  (Show Source):
You can put this solution on YOUR website!
e^(5ln3 - 4ln5)

Properties:
1) e^(lnx) = x
2) ln(x-y) = ln[x/y]
3) alnb = lnb^a

by #3 e^(ln3^5 - ln5^4)
simplify e^(ln 143 -ln625)
by rule #2 above e^(ln143/625)
by rule #1 above 143/625 because the e cancels the ln
answer is 143/625
e

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Can you show me how to solve e^(5ln3 - 4ln5) using the properties of logarithms? The answer is 243/625, but I want to know step by step how to get there? Thank you!
e%5E%285+ln+3+-+4+ln+5%29

highlight_green%28highlight_green%28e%5E%28ln+3%5E5+-+ln+5%5E4%29%29%29

e%5E%28ln+243+-+ln+625%29

highlight_green%28highlight_green%28e%5E%28ln+%28243%2F625%29%29%29%29

Let highlight_green%28highlight_green%28e%5E%28ln+%28243%2F625%29%29+=+x%29%29

Then ln+x+=+ln+%28243%2F625%29

Therefore, highlight_green%28highlight%28x+=+243%2F625%29%29