Chapter 11.5, Problem 20E

To determine

To find: The value of $\log 0.00009$ .

Answer to Problem 20E

The value of $\log 0.00009$ is $-3.9542$ .

Explanation of Solution

Given information:

The value of $\log 4=0.6021,\log 9=0.9542,\log 12=1.0792$ .

Here, $\log 0.00009$ can be written as,

  $\log 0.00009=\log \left(\frac{9}{10000}\right)$

Now by log property,

  $\begin{array}{c}\log 0.00009=\log \left(\frac{9}{10000}\right)\\ =\log 9-\log 10000\\ =\log 9-\log \left({10}^4\right)\end{array}$

On substituting the given values,

  $\begin{array}{c}\log 9-\log \left({10}^4\right)=\log 9-4\log 10\\ =\log 9-4\\ =0.9542-4\\ =-3.9542\end{array}$

Therefore, the value of $\log 0.00009$ is $-3.9542$ .