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Is a logarithm an irrational number?
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.
Is it possible for a logarithm to equal a negative 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.
Why is log -10 display an error on the calculator?
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...
What are some examples of logarithms?
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.
What irrational number is the base of a natural logarithm?
The number is called e, and it is approximately equal to 2.718.
