Question 63583: Expand and simplify: ln(xe)
All the sample problems have ln(ex) so is there a difference when the two letters are reversed? Thanks so much! Answer by venugopalramana(3286) (Show Source):
You can put this solution on YOUR website! Expand and simplify: ln(xe)
All the sample problems have ln(ex) so is there a difference when the two letters are reversed? Thanks so much!
THE ANSWER DEPENDS ON YOUR TYPING ACCURACY!
LET ME ASSUME DIFFERENT POSSIBILITIES IN THAT
1.YOU REALLY MEANT WHAT YOU TYPED..THAT IS
LN(XE) AND LN(EX)....THEN BOTH ARE SAME
AS YOU KNOW LN(AB)=LN(A)+LN(B)
HENCE LN(XE)= LN(X)+LN(E)=LN(E)+LN(X)=LN(EX)
2.YOU TYPED ERROEOUSLY..
A)IT IS LN(X^E) AND LN(E^X)
THEN THEY ARE NOT SAME
LN(X^E) = E*LN(X)
LN(E^X)=X*LN(E)=X*1=X
B)IT IS LOG TO BASE X OF E AND LOG TO BASE E OF X ..
THEN THY ARE NOT SAME
WHY I MENTIONEDTHIS POSSIBILITY IS THAT REFERENCE YOU MADE BOUT YOUR BOOK.
GENERALLY IN BOOKS HEN LOGS ARE TAKEN TO BASE E , IT IS REPRESENTED AS LN(...)
AND WHEN LOGS ARE TAKEN TO BASE 10 , IT IS REPRESENTED AS LOG(....)
