The log function, often known as the logarithm function, is used in most mathematical issues. The log function, also known as the logarithmic function, is commonly employed to minimize or restrict the complexity of mathematical problems. This is accomplished by using its well-defined characteristics to reduce the mathematical operations of multiplication to addition and division to subtraction. We will go through how to find the logarithm function by utilizing the value log infinite. In general, logarithms are divided into two types: common logarithmic functions and natural logarithmic functions. Common logarithmic functions: The log function with base 10 is the common logarithmic function. Natural logarithmic functions: The log function with base ‘e’ is the natural logarithmic function. The formula derived for calculating any log function in the base e is given below:
If log k c = d, then d k = c, In the formula mentioned above, ‘d’ is the logarithm of a number represented by ‘c,’ and the base of the log function is ‘k,’ which can be replaced either by the value ‘10’ or ‘e.’ The value of ‘k’ can range till infinity, but it can never be ‘1’. The main purpose of this article is to make the readers aware of what infinity is and its value in the logarithmic function.
Let us assume that log infinity is equivalent to log(p). Now, as we increase the value of p to infinity, the value of log(p) also increases and extends to infinity. This may be at a fast pace or a slower rate. This is the concept to calculate the value of log infinity. We should all be aware that infinity is expressed as ∞ (a sleeping number 8 like symbol). As stated above, there are two possible values of logarithmic functions. First is the common base 10, and the second is the natural base e. Let us determine the value of log infinity one at a time:
We can denote log infinity to the base 10 in two possible ways that are log10∞ and log ∞. Now according to the definition of logarithmic function as stated before, we conclude that Base = k, which is equal to 10 in this case. Therefore, 10 k = ∞. So, we can calculate that 10^∞ will be infinity as the value of ‘p’ approaches infinity; the value of the function also reaches infinity. Therefore, we can conclude that log10 = infinity (∞).
The natural log or the log with base e is always denoted using the notation, loge ∞ , or it can also be expressed as ln (∞). As we increase the value of variable ‘p’, slowly or swiftly towards infinity, the value of logarithmic function also increases to infinity, respectively. Loge ∞ = ∞, or ln (∞) = ∞ We can conclude that both the natural logarithm as well as the common logarithm value for infinity converse is at the same value, i.e., infinity. In similar ways, different values of logarithmic functions can be calculated and used to solve related problems.