# Math Help - Approximating the value of a logarithm by trial and error

1. ## Approximating the value of a logarithm by trial and error

use systematic trial and error to evaluate log50.

2. 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