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Many mathematicians used logarithms to transform multiplication and division problems into addition and subtraction problems prior to the calculus era. The power is raised to some numbers in logarithms, which is usually the base number. Then it can return a different number. It is the exponential function’s inverse function. The log Base 2 Binary base logarithm is a format that is also very useful in the computer field.
Binary logarithm
The binary logarithm is a variant of the base-2 logarithmic function. That means we’ll have expressions of the form x , and we’ll have to figure out how high we should raise 2 to get x. We can easily see that 4 log2 4 = 2.
Logarithm function
The logarithm function is computed as the inverse function of exponentiation in mathematics. In simple terms, the logarithm is the power to which a number must be raised to obtain a different value. The following is a general definition:
Where is the base and x is the value in exponent form, the equivalent expression is:
ax=y
Common Logarithm function: The common logarithmic function is a very popular logarithmic function with a base of ten. It’s commonly abbreviated as 10 or simply log.
Natural Logarithm function: The natural logarithmic function is the logarithmic function to the base e. It is abbreviated as loge or ln.
Log base 2 explanation
A binary logarithm is also known as log base 2 or log 2. It is equal to the inverse of the power of two functions. According to the general logarithm, we have exponential form for every real number N.
N=ax
Here, is a positive real number that is referred to as the base. And the exponent is x. Then it’s written like this:
The power to which the number 2 is raised to get the value of N is called log base 2. The log base 2 functions for any real number x are:
2x=N
It should be noted that the base 0 logarithm does not exist. In addition, in the real number system, negative logarithms are not defined.
Log Base 2 rules
Rules for log Base 2 given below
Product rule
Quotient rule
Power rule – Multiply the exponents and raise the exponential expression to the power.
Zero exponent rule
Change of base rule
What is log base 0
The value of log 0 is undefined. The value of log 0 is unknown. It’s not a real number because nothing can be raised to the power of anything else to get zero. No matter what the base of the logarithm is, log 1= 0 means that the logarithm of 1 is always zero.
Only for b>0 is the logarithmic function logab defined if
ax=0,100=0
,
Where x does not exist, finding the value of x is impossible. As a result, the base 10 of the logarithm of zero is unknown.
Conclusion
In this article we learned that the binary logarithm is the logarithm in base 2 in mathematics (n ). The binary logarithm is commonly abbreviated as lg n. It is equal to the inverse of the exponential function2nBecause it is so closely related to the binary numeral system, binary logarithm is frequently used in computer science and information theory. In information theory.
Binary logarithms can be used to calculate the length of a number’s representation in the binary numeral system, or the number of bits required to encode a message. They count the number of steps required for binary search and related algorithms in computer science.
