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

## 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 $\Delta S = {k}_{B} \ln \Omega$, the microstates equation for entropy.

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 ${10}^{10}$.
${10}^{- 138.265} = y$
$\implies {10}^{- 38.265 - 100} = y$
$\implies {10}^{- 38.265} / \left({10}^{100}\right) = y$
Since ${10}^{- 38.265} = 5.433 \times {10}^{- 39}$, $\textcolor{b l u e}{y = 5.433 \times {10}^{- 139}}$.