Without using Wolfram Alpha, evaluate $log_10(y) = -138.265$ ? The answer is not $0$ .

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It's easy to do it in Wolfram Alpha, but how could I simplify it so that it's able to be evaluated on a TI-83 calculator? There's a limit to how large or small the displayed numbers can be.

This is useful, for example, when you evaluate $DeltaS = k_BlnOmega$ , the microstates equation for entropy.

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Answer 1 · 2016-08-25T02:31:09

Hm, you know what, it would easier to just evaluate part of it on a calculator, and do the rest of it using factors of $10^10$ .

$10^(-138.265) = y$

$=> 10^(-38.265 - 100) = y$

$=> 10^(-38.265)/(10^(100)) = y$

Since $10^(-38.265) = 5.433xx10^(-39)$ , $color(blue)(y = 5.433xx10^(-139))$ .