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I need to solve this equation numerically, but I don't have access to any software:

$$2^{1-t} \log \tfrac12 = a(t) \log a(t)$$

where $a(t):= 2^{-t} + \tfrac12$.

The logs are natural logarithms.

Thanks for your help!

Ilmari Karonen
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Frank
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  • You can access the internet, apparently. https://www.google.com/search?q=calculator&btnG=Go – copper.hat Oct 06 '13 at 22:42
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    If I was absolutely sure I knew what you were trying to solve (solve for $t$, $a(t)$ ...?, any particular method?, is this typeset accurately?...) I could probably point you to some software, maybe even online. – J. W. Perry Oct 06 '13 at 22:46
  • I am trying to solve for t. I only used a(t) to make the expression clearer. There was a typo which I have corrected now. – Frank Oct 06 '13 at 23:06
  • Wolfram Alpha came up with $t \approx 2.42397516638965$ but I haven't checked it. – littleO Oct 07 '13 at 00:19

1 Answers1

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Since you can use the web, you do have access to Wolfram Alpha, which says the answer is approximately $t \approx 2.42397516638965$.

Ps. If you'd like to inspect the solution visually, you can also tell Wolfram Alpha to plot each side of your equation, giving you a pretty picture where you can see where the lines cross:

plot of 2^(1-t) * log(1/2) and (2^(-t) + 1/2) * log(2^(-t) + 1/2) from 2 to 3

This can sometimes be useful e.g. for checking that there really are no other solutions.

Ilmari Karonen
  • 26,117
  • Thanks a lot. I did spent quite a while trying to find software that would accept my equation online but didn't come across this one! – Frank Oct 06 '13 at 23:16