Approximating the value of a logarithm by trial and error

Quote:

Originally Posted by math123456

use systematic trial and error to evaluate log50.

By trial and error you have to find $x$ (approximatly) such that:

$10^x=50$

or dividing by $10$ :

$10^{x-1}=5$

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

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

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

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

CB