How to Derive Value of Log Infinity
To derive the value of log infinity we will use the basic formula of converting Logarithm to exponent or vice versa i.e., bx = y ⇔x = Logb y. The value of loge ∞ and log10 ∞ both are infinity as infinity is the only value that is raised to any number gives infinity. Below we will derive the value of Log infinity for both Common Logarithm and natural logarithm.
Derivation of Value of Loge Infinity
To derive loge ∞ i.e., infinity we will use the log to exponent conversion formula.
Let p = loge ∞
We know that,
bx = y ⇔x = Logb y
By using above formula
p = loge ∞ ⇔ ep = ∞
The above expression satisfies only when the value of p is infinity. So, the value of Loge infinity is infinity.
Loge Infinity = Infinity
or
ln infinity = infinity
Derivation of Value of Log10 Infinity
To derive loge ∞ i.e., infinity we will use the log to exponent conversion formula.
Let p = log10 ∞
We know that,
bx = y ⇔x = Logb y
By using above formula
p = log10 ∞ ⇔ 10p = ∞
The above expression satisfies only when the value of p is infinity. So, the value of Log10 infinity is infinity.
Log10 Infinity = Infinity
or
Log Infinity = Infinity
Value of Log Infinity
Value of Log10 ∞ = ∞ or Loge ∞ = ∞.
In both types of logarithms, i.e., natural logarithm and common logarithm, the value for infinity is infinity. The value of log of infinity is infinity, irrespective of the base of the logarithm. In this article, we will discuss the value of log infinity along with a basic understanding of logarithms. We will also discuss how to derive Log infinity, both Loge infinity and Log10 infinity.