Question

Convert the following into exponential form.
\[{{\log }_{2}}32=5\]

Answer 1

Hint: We are given a question based on conversion from logarithm to exponential. We will make use of the logarithmic property in order to carry out the required conversion. We know the property that a logarithm function of the form, \[{{\log }_{a}}b=c\] can be expressed as \[{{a}^{c}}=b\], where ‘a’ is the base. We will substitute the value from the given expression and hence, we will have the given expression in logarithmic form to exponential form.

Complete step by step answer:
According to the given question, we are given a question having a logarithm function. We are asked in the question to convert the given expression in logarithmic function to exponential form.
The expression that we are given is,
\[{{\log }_{2}}32=5\]
We will use the property of the logarithms to do the desired conversion.
We know that, the logarithm function of form, \[{{\log }_{a}}b=c\] can be written in other form (exponential form) as \[{{a}^{c}}=b\]. Here. ‘a’ serves as the base.
For example - if we have \[{{\log }_{5}}25=2\], we can write this in the exponential form as, \[{{5}^{2}}=25\], where 5 is the base here.
So, we will substitute the value from the given expression into the above formula and we will have the required conversion and so we have,
\[{{\log }_{2}}32=5\]
\[\Rightarrow {{2}^{5}}=32\]
And 2 is the base here.
Therefore, the exponential form of the given expression is \[{{2}^{5}}=32\].

Note: While doing the conversion, do not get confused with the terms and write it in incorrect order. As then the expression obtained would not even comply. So, the values must be carefully substituted in the formula and it should be done step wise. Also, after obtaining the required expression check if it makes sense that way it will get verified as well.