Question

If ${\log _3}5 = x$, express it in exponential form.

Answer 1

Hint: The given problem deals with the use of logarithms. It focuses on the basic definition of the logarithm function. We can solve the problem easily by converting the given logarithmic form into exponential form. For this, we need to have knowledge of interconversion of logarithmic function to exponential function.

Complete solution:
Given question requires us to solve the logarithmic equation ${\log _3}5 = x$ to find the value of variable x.
Now, ${\log _3}5 = x$ can be easily changed into exponential form by understanding the interconversion between the logarithmic and exponential function.
The exponential form ${a^n} = b$ where base $ = a$, exponent$ = n$, value$ = b$ is written as ${\log _a}b = n$ in logarithmic form, read as log of ‘b’ to base ‘a’ is equal to ‘n’.
Therefore, the logarithmic form, read as log of ‘b’ to base ‘a’ is equal to ‘n’ can be written as ${a^n} = b$ in exponential form.
So, ${\log _3}5 = x$ can be written in exponential form as $5 = {3^x}$.
So, changing the sides of equation, we get,
$ \Rightarrow {3^x} = 5$

Hence, the logarithmic function ${\log _3}5 = x$ can be expressed in exponential form as ${3^x} = 5$.

Note:
We should note that these kinds of problems will be solved only using different identities of logarithms and exponents.
Example-
1. $a^{mn}=a^m.a^n$
2. $\log {mn} =\log m + \log n$