Question

How to find the log of a given number.

Answer 1

Hint: Generally, for finding the log of a given number, it is prescribed to break the log of a number to the form for which you can predict its value using the properties of a logarithmic function. Also, a log table can be used if needed.

Complete step-by-step answer:

To find the log of a number, we need to interpret what the log of the number actually refers to in exponential terms. Suppose we have $y={{\log }_{b}}a$ , this is equivalent to ${{b}^{y}}=a$ in exponential form.

So, in some cases you might predict the log of a number just by using the exponential equivalent. For example: we will find the value of y, provided $y={{\log }_{10}}100$ . Now the exponential equivalent of $y={{\log }_{10}}100$ is ${{10}^{y}}=100$ , looking at which we can say that y=2.

In some other cases you might have to use the properties like:

${{\log }_{a}}x+{{\log }_{a}}y={{\log }_{a}}xy$

${{\log }_{a}}x-{{\log }_{a}}y={{\log }_{a}}\dfrac{x}{y}$

${{\log }_{{{a}^{b}}}}x=\dfrac{1}{b}{{\log }_{a}}x$

${{\log }_{a}}{{x}^{b}}=b{{\log }_{a}}x$

However, to make the use of properties more effective, it is better that you learn the log of natural numbers till 5. In the cases where you can neither get to a result using the exponential equivalent nor the properties there, you need to use the logarithmic table.


Note: Generally, the theory questions that we come across in our day to day life don’t need a logarithmic table to be solved; however, for solving the experimental data, you might require a logarithmic table.