SOLUTION: Suppose that x=ln(A) and y=ln(B) . Write the following expressions in terms of x and y (so you cannot have A or B anywhere in your answers). ln(AB)= ln(A)/ln(B)= AB= Please

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Suppose that x=ln(A) and y=ln(B) . Write the following expressions in terms of x and y (so you cannot have A or B anywhere in your answers). ln(AB)= ln(A)/ln(B)= AB= Please      Log On


   

Question 1000305: Suppose that x=ln(A) and y=ln(B) . Write the following expressions in terms of x and y (so you cannot have A or B anywhere in your answers).
ln(AB)=
ln(A)/ln(B)=
AB=
Please help, I do not understand these. Thanks!
Answer by ikleyn(52804) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.  ln(AB) = ln(A) + ln(B) = x + y.

     First equality is the basic property of the logarithm.  Are you familiar with it?

     The second equality is true because  ln(A) = x  and  ln(B) = y,  which is given.  I simply made a substitution here.


2.  ln(A)/ln(B) = x%2Fy.

     Simply substitute  x  and  y  instead of  ln(A)  and  ln(B)  into the numerator and denominator.


3.  A%2AB = e%5Ex . e%5Ey.

     Since  ln%28A%29 = x,  you have  A = e%5Ex.

     Since  ln%28B%29 = y,  you have  B = e%5Ey.

     Then substitute this into  A%2AB.


That is all,  my dear.

Look into my lessons
    - WHAT IS the logarithm 
    - Properties of the logarithm
in this site.

It is free of charge and without registration.