Question

How do you write ${\log _3}243 = 5$ 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 step-by-step answer :
Given question requires us to express ${\log _3}243 = 5$ in exponential form.
So, ${\log _3}243 = 5$ 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.
In this case, the base of logarithm is $3$, as ${\log _3}243 = 5$ is read as log of ‘$243$’ to base ‘$3$’ is equal to ‘$5$’.
Hence, ${\log _3}243 = 5$ can be written in exponential form as ${3^5} = 243$.
So, the correct answer is “ ${3^5} = 243$.”.

Note : Logarithm is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number. Exponential form is a way of representing repeated multiplications of the same number by writing the number as a base with the number of repeats written as a small number to its upper right as power of the number.
The conversion of logarithmic form to exponential form is an easy task keeping in mind the readily interconvertible of the forms for a given number. We just need to have knowledge about the definitions of logarithms and exponents.