Log infinity value
Logarithmic function or log function is used to reduce the complexity of problems by reducing the division into subtraction and multiplication into addition by using the logarithmic function properties. A logarithm is classified into two types that are common logarithm function and natural logarithm function.
A natural logarithmic function can be defined as the log function with base 'e', and the common logarithmic function can be defined as the log function with base 10.
The symbol of infinity is '∞'. Suppose the log infinity as log(x). So, as the value of x increases infinitely, log(x) will increase infinitely.
Calculating the value of log infinity
Let's see how to calculate the log infinity value. We are discussing the way of finding the log infinity value using common log function and natural log function.
Value of loge infinity
It is also referred to as the log function of infinity to the base e. It is denoted as the loge∞, and it is also represented as the ln(∞).
Loge∞ = ∞ or, we can say that ln(∞) = ∞
Value of log10 infinity
The log function with base 10 is a common logarithmic function, and the log function of infinity to the base 10 is denoted as log ∞ or log10∞. As the logarithmic function definition, it is clear that -
Base, a =10 and 10x = ∞
So, the value of log infinity to the base 10 is -
Suppose that 10∞ = ∞, then it will be
Log10 ∞ = ∞
Both of the types of logarithmic function (common logarithmic function and natural logarithmic function) value of infinity have the same value.
Now, let's see some questions to understand this topic clearly.
Ques - 1) Evaluate limx -> ∞ ex
Ans - 1) When the value of x will be infinity, it becomes
e∞ = ∞
So, lim x -> ∞ ex = ∞
Ques - 2) Evaluate lim x -> -∞ ex
Ans - 2) When the value of x is negative infinity, it becomes
e-∞ = 0
So, lim x -> -∞ ex = 0
Ques - 3) Evaluate limx -> ∞ e-x
Ans - 3) When the value of x is infinity, it becomes
e-∞ = 0
So, limx -> ∞ e-x = 0
Ques - 4) Evaluate limx -> -∞ e-x
Ans - 4) When the value of x is negative infinity, it becomes
e-(-∞) = ∞
So, limx -> -∞ e-x = ∞