Why are logarithmic functions undefined for zero and negative inputs?

Originally Answered: In mathematics, why can’t you have a logarithm of a negative number? Because a logarithm is, by definition, the inverse of an exponential function. Assuming that the base is positive and that we are only considering real numbers, every power of the base is positive.

Why are logarithms of negative numbers not defined?

What is the logarithm of a negative number? Since the base b is positive (b>0), the base b raised to the power of y must be positive (by>0) for any real y. So the number x must be positive (x>0). The real base b logarithm of a negative number is undefined.

Why is the logarithm of 0 undefined?

log 0 is undefined. It’s not a real number, because you can never get zero by raising anything to the power of anything else. log 1 = 0 means that the logarithm of 1 is always zero, no matter what the base of the logarithm is. This is because any number raised to 0 equals 1.

Can logarithms have negative values?

You can’t take the logarithm of a negative number or of zero. 2. The logarithm of a positive number may be negative or zero.

Can a logarithmic equation have a negative solution?

Logarithms cannot have non-positive arguments (that is, arguments which are negative or zero), but quadratics and other equations can have negative solutions. Each log in the equation had the same base, and each side of the log equation ended up with the value, so the solution “checks”.

What is a negative logarithm?

Negative Log Definition A negative log is defined as the number of times required that 1 must be divided by the base in order to achieve the log number. So, -Log2(. 5) = 1. Since 1/2 = -. 5.

Can you have log base 0?

No logically log with base 0 is not possible for any number other than 0 itself. The mathematical meaning of logarithms would explain it better why. now 0 raised to anything(other than 0) will be 0 so logarithm(with base 0) of anything other than 0 would not be possible to find.

What makes a log negative?

log (1/a) = -log a means that the logarithm of 1 divided by some number is equal to the negative logarithm of that number. (This is the exactly the opposite of the rule governing exponents where a number raised to a negative number is equal to 1 divided by that number raised to that power.)

What does negative logarithm mean?

A negative log is defined as the number of times required that 1 must be divided by the base in order to achieve the log number. So, -Log2(. 5) = 1.

Can a logarithmic equation have a negative solution that is not extraneous?

Why do we need logarithms?

Logarithmic functions are important largely because of their relationship to exponential functions. Logarithms can be used to solve exponential equations and to explore the properties of exponential functions.

Why can’t we use negative numbers as base of logarithm?

So 0, 1, and every negative number presents a potential problem as the base of a power function. And if those numbers can’t reliably be the base of a power function, then they also can’t reliably be the base of a logarithm. For that reason, we only allow positive numbers other than 1 as the base of the logarithm.

Why Log(0) is not defined?

Why log (0) is not defined. The real logarithmic function log b (x) is defined only for x>0. We can’t find a number x, so the base b raised to the power of x is equal to zero: b x = 0 , x does not exist So the base b logarithm of zero is not defined. For example the base 10 logarithm of 0 is not defined:

Why is the log of a negative number undefined?

The logarithm of a negative number is not defined as a negative number is equal to the odd power of a negative number. For X to be negative in the earlier relation, a has to be a negative number and b has to be odd. If a were negative, for most values of X, there wouldn’t be a corresponding value for b. Why is log zero undefined?

What is the base b log of zero?

So the base b logarithm of zero is not defined. For example the base 10 logarithm of 0 is not defined: The limit of the base b logarithm of x, when x approaches zero from the positive side (0+), is minus infinity: