Question

How do you write the equation ${\log _{13}}(169) = 2$ in exponential form?

Answer 1

Hint: In this question we need to convert from logarithmic form to exponential form. To solve this type of question we need to know the definition of logarithmic and relation between logarithmic form and exponential form. This question is very easy and just requires definition. Please try yourself before looking at the complete solution once.

Complete step by step answer:
Let us try to convert the equation ${\log _{13}}(169) = 2$ in exponential form. To convert this we need to know the definition of logarithmic function. Before going to solve this we will recall the definition of logarithmic and its relation to exponential. The logarithmic is another way to write exponential in an efficient way, it means that logarithmic is inverse of exponential.
If we have any equation in exponential form such that ${b^y} = x$ then we have its logarithmic as ${\log _b}x = y$ where $x > 0,b > 0$ and $b \ne 1$.
Now, we will be convert our equation which is in logarithmic form to exponential form
${\log _{13}}(169) = 2$
From our equation we have
$
  x = 169 \\
  b = 13 \\
  y = 2 \\
 $
Now from the relation we can write a logarithmic equation in exponential form as ${b^y} = x$. From our above values of $x,\;y$ and $b$. This logarithmic ${\log _{13}}(169) = 2$ written as exponential form ${13^2} = 169$.

Hence the exponential form of ${\log _{13}}(169) = 2$ is ${13^2} = 169$.

Note: To solve this type of question which is asked to convert from logarithmic to exponential form are very easy generally students confused in getting the correct value of $b$ and $y$. Similarly, we are also asked to convert between exponential to logarithmic form. To solve this you need to know the relation between logarithmic and exponential form. Logarithmic use in mathematics, physics and chemistry is widespread.