How to Derive Value of Log 0
To derive the value of Log 0 we use the fundamental formula of conversion of logarithm to exponent or vice versa i.e., xa = q ⇔ a = logx q. The value of Loge 0 and Log10 0 both are not defined as we cannot have any number whose any power is equivalent to 0.
Derivation of Value of Loge 0
To derive the value of Loge 0 i.e., not defined we will use the log to exponent conversion formulae.
Let y = Loge 0
We know that,
xa = q ⇔ a = logx q
By the above formula
y = Loge 0 ⇔ ey = 0
We cannot find any value of y which satisfies ey = 0. So, the value of Loge 0 is undefined.
Value of Loge 0 = Undefined
or
Value of Loge 0 = ∞
Derivation of Value of Log10 0
To derive the value of Loge 0 i.e., not defined we will use the log to exponent conversion formulae.
Let y = Loge 0
We know that,
xa = q ⇔ a = logx q
By the above formula
y = Log10 0 ⇔ 10y = 0
We cannot find any value of y which satisfies 10y = 0. So, the value of Loge 0 is undefined.
Value of Log10 0 = Undefined
or
Value of Log10 0 = ∞
Value of Log 0
Value of log 0 is undefined. It is not a real number as we can never get zero by raising any power of any number. This can never be reached to zero but can be approached using negative power or infinitely large value. In this article, we will discuss the value of Log 0 along with basic understanding of logarithms. We will also discuss how to derive Log 0 both Log10 0 and Loge 0.
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