use systematic trial and error to evaluate log50.

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- Apr 21st 2009, 10:20 PMmath123456Approximating the value of a logarithm by trial and error
use systematic trial and error to evaluate log50.

- Apr 21st 2009, 10:40 PMCaptainBlack
By trial and error you have to find $\displaystyle x$ (approximatly) such that:

$\displaystyle 10^x=50$

or dividing by $\displaystyle 10$:

$\displaystyle 10^{x-1}=5$

start with $\displaystyle x=1$, then $\displaystyle 10^{x-1}=1$, which is too small,

next try $\displaystyle x=2$, then $\displaystyle 10^{x-1}=10$, which is too large

So for our next try we take $\displaystyle x=1.5$, then $\displaystyle 10^{x-1}=\sqrt{10}\approx 3.16$ which is too small

Now we know that the required $\displaystyle x$ is between $\displaystyle 1.5$ and $\displaystyle 2$, so for our next trial we use $\displaystyle x=1.75 $and carry on as above refining the interval containing the required solution.

CB