Usually, but not necessarily. A logarithm that is not an integer-value is irrational. For example log10100 = 2 which is a rational number. log1012 = 1.0791812460476... which is an irrational number.
Yes. The logarithm of 1 is zero; the logarithm of any number less than one is negative. For example, in base 10, log(0.1) = -1, log(0.01) = -2, log(0.001) = -3, etc.
In the real numbers, the logarithm is only defined for positive numbers. The logarithm of zero or a negative number is undefined. (For calculators who work with complex number, only the logarithm of zero is undefined.) This follows from the definition of the logarithm, as the solution of: 10x = whatever "Whatever" is the number of which you want to calculate the logarithm. Since 10x is always positive, that means you can't find an "x" such that the power results in a negative number, or in zero. The same applies if you use a base other than 10, for example the number e = 2.718...
A logarithm answers the question of how many times you must multiply a number by itself to get another number. For example, 3x3x3 is 9, so to get 9, the logarithm is 3.
The number is called e, and it is approximately equal to 2.718.
A logarithm is the exponent to which a number called a base is raised to become a different specific number. A common logarithm uses 10 as the base and a natural logarithm uses the number e (approximately 2.71828) as the base.
That is a logarithm to the base "e", where "e" is a number that is approximately 2.718.
A number for which a given logarithm stands is the result that the logarithm function yields when applied to a specific base and value. For example, in the equation log(base 2) 8 = 3, the number for which the logarithm stands is 8.
An antilogarithm is the number of which the given number is the logarithm (to a given base). If x is the logarithm of y, then y is the antilogarithm of x.
Usually, but not necessarily. A logarithm that is not an integer-value is irrational. For example log10100 = 2 which is a rational number. log1012 = 1.0791812460476... which is an irrational number.
The "base of the natural logarithm" is the number known as "e". It is approximately 2.718.
maths
The Logarithm of a number is the converse of its logarithmic value..
Within the real numbers, the logarithm of negative numbers is not defined.
Rational.
Yes. The logarithm of 1 is zero; the logarithm of any number less than one is negative. For example, in base 10, log(0.1) = -1, log(0.01) = -2, log(0.001) = -3, etc.
In the real numbers, the logarithm is only defined for positive numbers. The logarithm of zero or a negative number is undefined. (For calculators who work with complex number, only the logarithm of zero is undefined.) This follows from the definition of the logarithm, as the solution of: 10x = whatever "Whatever" is the number of which you want to calculate the logarithm. Since 10x is always positive, that means you can't find an "x" such that the power results in a negative number, or in zero. The same applies if you use a base other than 10, for example the number e = 2.718...