Question

How do you write \[\log x = y\] in exponential form?

Answer 1

Hint: We are given an equation and asked to write the equation in exponential form. For this, you will need to recall the concepts of log and antilog and apply those to write the equation in exponential form. And you can also write terms on L.H.S and R.H.S in exponential form and check the result.

Complete step-by-step answer:
Given the equation \[\log x = y\] .
We are asked to write the given equation in exponential form.
The given equation is,
 \[\log x = y\]
Taking antilog we get,
 \[x = {\text{antilog}}\left( y \right)\] (i)
Inverse of a log function is exponential so, we can write,
 \[{\text{antilog}}\left( y \right) = {e^y}\]
Putting this value in equation (i) we get,
 \[x = {e^y}\]
Therefore, the exponential form of \[\log x = y\] is \[x = {e^y}\] .
Alternative method:
We are given,
 \[\log x = y\]
So, if we write the equation in exponential form on both sides we get,
 \[{e^{\log x}} = {e^y}\] (ii)
The term \[{e^{\log x}}\] can be written as,
 \[{e^{\log x}} = x\]
Putting this value in equation (ii) we get,
 \[x = {e^y}\]
Hence, the exponential form of \[\log x = y\] is \[x = {e^y}\] .
So, the correct answer is “ \[x = {e^y}\] ”.

Note: Remember that logarithm is inverse of exponential. Also, there are few basic logarithm formulas which should be remembered for questions related to logarithm. Logarithm can be defined as a power to which a number is raised to get some other values. There are two types of logarithms, these are common logarithm and natural logarithm. The common logarithm is the logarithm with base \[10\] and it is written as \[{\log _{10}}\] , the base \[10\] means how many times the number \[10\] should be multiplied to get the given number. The natural logarithm is logarithm with base \[e\] and it is written as \[{\log _e}\] or \[\ln \] .