What is Logarithm?
Logarithm is a mathematical function used to measure the relative size of two quantities. It is the inverse of the exponential function, which means that if we have y = a^x, then x = log_a(y).
The most commonly used logarithm is the base 10 logarithm, also known as the common logarithm. It is denoted by log(x) or log10(x), where x is any positive number.
Log1=0?
Yes, log1 is equal to 0. This is because any number raised to the power of 0 is equal to 1. Therefore, if we have log_a(1) = x, then a^x = 1, which means that x = 0.
For example, log10(1) = 0, log2(1) = 0, and log3(1) = 0.
Log0=?
The value of log0 is undefined or “not a number” (NaN). This is because there is no positive number that can be raised to the power of 0 and give us 0 as the result.
For example, if we have log_a(0) = x, then a^x = 0. However, there is no value of x that can satisfy this equation. Therefore, log0 is undefined.
Why is Log0 Undefined?
The reason why log0 is undefined is because the logarithmic function is only defined for positive numbers. This is because the exponential function is only defined for positive numbers as well.
If we have a negative number raised to the power of a fraction or a decimal, then we get a complex or imaginary number. Therefore, it does not make sense to talk about the logarithm of a negative number.
Similarly, if we have 0 raised to the power of a fraction or a decimal, then we get 0 as the result. However, 0 is not a positive number and therefore, it does not make sense to talk about the logarithm of 0.
Conclusion
In conclusion, log1 is equal to 0 because any number raised to the power of 0 is equal to 1. However, log0 is undefined or “not a number” because there is no positive number that can be raised to the power of 0 and give us 0 as the result. Therefore, it is important to understand the properties and limitations of logarithmic functions in order to use them effectively in mathematics and other fields.
