The logarithm function, abbreviated as log function, is utilized in almost all mathematical problems. The log function, also referred to as the logarithmic function, is frequently used to reduce or limit the difficulty of mathematical issues. This is done by utilizing its well-defined features to simplify multiplication to addition and division to subtraction. We will see how to find the logarithm function using the value log zero. The formula derived for calculating any log function in the base e is given below:
logks = r, then kr = s,
In the formula stated, ‘r’ is the logarithm of a number represented by ‘s,’ 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 go all the way to infinity, but it will never be ‘1'. The primary goal is to educate readers on the concept of infinity and its value in the logarithmic function.
Logarithms are broadly classified into two types: common logarithmic functions and natural logarithmic functions. The log function with base 10 is the common logarithmic function. The log function with base e is the natural logarithmic function.
Now that we know the rudimentary concept of log and exponents let us derive the value of log 0. For this, initially, let us consider that log 0 is equivalent to log(s). The rate of logarithmic function may be fast-paced or slow-paced. As previously stated, logarithmic functions can have two potential values: the common base 10 and the natural base e. Let us calculate the value of log zero one method at a time:
We can denote log zero to the base 10 in two possible ways that are log10 (0) and log (0). Now according to the definition of logarithmic function as stated before, we conclude that
The base of the log is k = 10, the value of s = 0; if we solve this, we get
10k = s, but we can only express the logarithmic value if the value of ‘s’ is greater than 0. But in this case, ‘s’ = 0. Therefore, the value of the log cannot be computed hence,
Log10 (0) is undefined.
Again, using the concept of solving logarithmic functions, loge (0) = se. Here, in the natural log,
The base of the log is k = e, the value of s = 0; if we solve this, we get
es = 0, again we get an equation in which any value of s cannot satisfy the equation hence,
Log e (0) is also undefined.
We may deduce that the natural logarithm and common logarithm values for 0 intersect at the same point, i.e., undefined. Similarly, alternative logarithmic function values can be derived and utilized to solve related issues.
1. Calculate the value of k if logk64= 2
Sample Answer: Comparing logk64= 2 with logks = r, we get:
S= 64 and r= 2
Therefore, on substituting the values in the formula kr= s K²= 64
So, k= 8.