# Approximating the value of a logarithm by trial and error

• Apr 21st 2009, 10:20 PM
math123456
Approximating the value of a logarithm by trial and error
use systematic trial and error to evaluate log50.
• Apr 21st 2009, 10:40 PM
CaptainBlack
Quote:

Originally Posted by math123456
use systematic trial and error to evaluate log50.

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