SOLUTION: Ln(x)=2Ln(x)-Ln(y)+Ln(c) Answer is given as y=cx Directions are to solve for y. Problems that are not given in numbers always give me trouble.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Ln(x)=2Ln(x)-Ln(y)+Ln(c) Answer is given as y=cx Directions are to solve for y. Problems that are not given in numbers always give me trouble.      Log On


   

Question 127412: Ln(x)=2Ln(x)-Ln(y)+Ln(c) Answer is given as y=cx
Directions are to solve for y. Problems that are not given in numbers always give me trouble.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Ln%28x%29=2Ln%28x%29-Ln%28y%29%2BLn%28c%29 Start with the given equation


0=2Ln%28x%29-Ln%28y%29%2BLn%28c%29-Ln%28x%29 Subtract Ln(x) from both sides


Ln%28y%29=2Ln%28x%29%2BLn%28c%29-Ln%28x%29 Add Ln(y) to both sides


Ln%28y%29=Ln%28x%5E2%29%2BLn%28c%29-Ln%28x%29 Now rewrite 2Ln%28x%29 as Ln%28x%5E2%29 by using the identity y%2ALn%28x%29=Ln%28x%5Ey%29


Ln%28y%29=Ln%28x%5E2c%2Fx%29 Rewrite the right side by using the identities Ln%28x%29%2BLn%28y%29=Ln%28x%2Ay%29 and Ln%28x%29-Ln%28y%29=Ln%28x%2Fy%29


Ln%28y%29=Ln%28xc%29 Simplify


e%5E%28Ln%28y%29%29=e%5E%28Ln%28xc%29%29 Now raise both sides as powers with "e" as the base


y=xc Simplify. Remember, e%5E%28Ln%28y%29%29=y (ie these two functions undo each other and cancel themselves out)