Expert: Paul Klarreich - 9/9/2007

Question
Hi Paul. I have recently started an HNC after 25 years out of the loop. Looking for a solution/pointer to the following. Solve for "t" 1.5=4e^2t. Logs comes to mind but I darned if I can remember. Thanks. Kev.

Answer
Questioner:   Kev
Category:  Advanced Math
Private:  No
 
Subject:  Logs and powers
Question:  Hi Paul. I have recently started an HNC after 25 years out of the loop. Looking for a solution/pointer to the following. Solve for "t" 1.5=4e^2t. Logs comes to mind but I darned if I can remember. Thanks. Kev.
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Hi, Kev,

You are right -- it has something to do with logs.

In your equation:

1.5 = 4 e^2t

Divide by 4:

e^2t = 1.5/4 = 0.375

Take the natural log (ln) of both sides. (On your windows calculator, just enter 0.375 and hit the LN button.)

[Of course,  ln( e^something) = something ]

2t = -0.980829253011726236856451127452

Divide by 2:

t = -0.490414626505863118428225563726