Question

How do you simplify \[{e^{\ln x}}\]?

Answer 1

Hint:
The given question is to simplify the given expression which consists of logarithmic and exponent. Logarithm is nothing but the exponent or power to which a base must be raised to yield a given number. The given expression consists of logarithmic and exponential function and we have to simplify that.

Complete step by step solution:
The given question is about the logarithmic and exponential functions. Logarithmic function is the function in which power or exponent to which the base must be raised to get the given number and exponential function is the antilog.
Logarithmic function is the inverse of antilog and exponential function is the antilog. Therefore, logarithmic function and the exponential functions are inverse of each other and get cancelled out with each other and we are left with the power or exponent which also becomes base after the cancellation of logarithm and exponential with each other.
The given question is to simplify \[{e^{\ln x}}\]. Since we have discussed that logarithmic function and exponential functions are inverse of each other. Therefore, we are left with power or exponent in the base and hence we are left with \[x\] in the base only.
Therefore, \[{e^{\ln x}} = x\]

Therefore, after simplification of \[{e^{\ln x}}\] we get \[x\].

Note:
In the given question, we had to find out the value of the expression which is the function of logarithm and exponent. Logarithm is the inverse of exponential function and exponential function is the function which is known as antilog. Since, antilog and log or exponent and logarithm are inverse of each other and hence, they got cancelled with each other and we are left with the exponent or power only in the base.