• Support PF! Buy your school textbooks, materials and every day products Here!

E^(2lnt) = t^2 Whyyy?

  • #1
ok guys, i dont see how e^2ln|t| = t^2 can someone explain it to me please? Seems so easy but i dont see it.
 

Answers and Replies

  • #2
ok, so far i tried this. I know e^(lnx) = x


so, i broke the e^(2ln|t|) into to parts:


e^2 times e^(ln|t|) which equals t (from the top identity)


so im left with e^2 times t. which is te^2

but the book says it equals t^2..so what happened to the e? (exponential function)
 
  • #3
429
0
CinderBlockFist said:
ok, so far i tried this. I know e^(lnx) = x


so, i broke the e^(2ln|t|) into to parts:


e^2 times e^(ln|t|) which equals t (from the top identity)


so im left with e^2 times t. which is te^2

but the book says it equals t^2..so what happened to the e? (exponential function)
you have

e^2 e^(ln t) = e^(2+ln t),

which is incorrect.


you want to use the properties:


a ln b = ln b^a

and

e^ln a = a.


the rest should be straightfoward.
 
Last edited:
  • #4
Tom Mattson
Staff Emeritus
Science Advisor
Gold Member
5,500
7
First look at this rule for logarithms:

[itex]\log_b(a^x)=x\log_b(a)[/itex].

Now apply that to your exponent:[itex]2\ln |t|[/itex]. What do you get?

Then note that [itex]f(x)=\ln (x)[/itex] and [itex]g(x)=e^x[/itex] are inverse functions, which means that [itex]f(g(x))=g(f(x))=x[/itex].

Those two rules together will give you the answer.
 
  • #5
SWEEET! THANK YOU GUYS. I got my laws of exponents mixed up. :yuck:
 

Related Threads for: E^(2lnt) = t^2 Whyyy?

Replies
1
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
5
Views
6K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
10K
Replies
1
Views
1K
  • Last Post
Replies
5
Views
2K
Replies
5
Views
2K
Top