Question

How do you change \[{{4}^{-3}}\] = \[\dfrac{1}{64}\] into log form?

Answer 1

Hint: For these kinds of problems where we have to convert into logarithmic form from the given form we have to know the basic rule of logarithmic operations to convert it from one form to another as \[{{a}^{n}}=b\] in logarithmic form can be written as \[lo{{g}_{a}}b=n\]. In this case it’s given as \[{{4}^{-3}}\] = \[\dfrac{1}{64}\]. We also have to know the standard representation of the log values.

Complete step by step solution:
We have asked here to change \[{{4}^{-3}}\] = \[\dfrac{1}{64}\] into log form.
We know from the standard forms to change to the log forms,
As \[{{a}^{n}}=b\] in logarithmic form can be written as \[lo{{g}_{a}}b=n\]
Here it can be observed that the values of a, b and n as below,
a = 4, b = \[\dfrac{1}{64}\] and n = -3
So, for the given question the converted form can be written as below,
Hence, \[{{4}^{-3}}\] = \[\dfrac{1}{64}\] can be written as \[lo{{g}_{4}}\dfrac{1}{64}=-3\]
The changed form of the given problem in log form is \[lo{{g}_{4}}\dfrac{1}{64}=-3\]

Note: The knowledge of converting a power term in log form is very important as we should know that \[{{a}^{n}}=b\] in logarithmic form can be written as \[lo{{g}_{a}}b=n\] in logarithmic form. In these kinds of questions students can go wrong in taking the values of a, b and n. so please be careful in taking the values. It is also important for us to represent the given problem in standard form only as any mistake can lead to the wrong answer.