SOLUTION: 5^(x-1)=3^x Find x I tried to solve using log and i couldn't find x. Can anybody help on this? Thank you~!

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 5^(x-1)=3^x Find x I tried to solve using log and i couldn't find x. Can anybody help on this? Thank you~!      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 193270: 5^(x-1)=3^x Find x I tried to solve using log and i couldn't find x. Can anybody help on this? Thank you~!
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
5%5E%28x-1%29=3%5Ex Start with the given equation.


log%2810%2C%285%5E%28x-1%29%29%29=log%2810%2C%283%5Ex%29%29 Take the log of both sides


%28x-1%29log%2810%2C%285%29%29=x%2Alog%2810%2C%283%29%29 Pull down the exponents


x%2Alog%2810%2C%285%29%29-log%2810%2C%285%29%29=x%2Alog%2810%2C%283%29%29 Distribute


-log%2810%2C%285%29%29=x%2Alog%2810%2C%283%29%29-x%2Alog%2810%2C%285%29%29 Subtract x%2Alog%2810%2C%285%29%29 from both sides.


-log%2810%2C%285%29%29=x%28log%2810%2C%283%29%29-log%2810%2C%285%29%29%29 Factor out the GCF "x" on the right side


-log%2810%2C%285%29%29=x%2Alog%2810%2C%283%2F5%29%29 Combine the logs on the right side using the identity log%28b%2C%28A%29%29-log%28b%2C%28B%29%29=log%28b%2C%28A%2FB%29%29


-log%2810%2C%285%29%29%2Flog%2810%2C%283%2F5%29%29=x Divide both sides by log%2810%2C%283%2F5%29%29.


3.15066=x Evaluate the right side (using a calculator). Note: the value of "x" is now approximate


x=3.15066 Rearrange the equation


So the solution is approximately x=3.15066