Homework Help: E^(2lnt) = t^2 Whyyy?

CinderBlockFist · Sep 13, 2005

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.

CinderBlockFist · Sep 13, 2005

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)

Brad Barker · Sep 13, 2005

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.

Tom Mattson · Sep 13, 2005

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.

CinderBlockFist · Sep 13, 2005

SWEEET! THANK YOU GUYS. I got my laws of exponents mixed up. :yuck:

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Homework Help: E^(2lnt) = t^2 Whyyy?

CinderBlockFist

CinderBlockFist

Brad Barker

Tom Mattson

CinderBlockFist