Why does ln have to be positive?

The outside function is ln x, and we know that to be in the domain of ln x, x must be a positive number. This tells us that the only x which can be in the domain of ln(x2) are those for which x2 is a positive number.

Can you ln a negative number?

The natural logarithm function ln(x) is defined only for x>0. So the natural logarithm of a negative number is undefined.

Why is the log of a negative number undefined?

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.

Can a logarithmic equation have a negative number as a 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”.

Can ln only positive?

The argument of a log function can only take positive arguments. In other words, the only numbers you can plug into a log function are positive numbers.

Why is ln used in math?

A logarithm (LN) is a concept in mathematics that denotes the number of times a number has to be multiplied by itself in order to arrive at a specified value. In mathematical terms, a logarithm of a number is the exponent that is used to raise another number, the base, in order to arrive at that number.

Where is ln defined?

The natural logarithm can be defined for any positive real number a as the area under the curve y = 1/x from 1 to a (with the area being negative when 0 < a < 1).

Is ln 0 defined?

What is the natural logarithm of zero? The real natural logarithm function ln(x) is defined only for x>0. So the natural logarithm of zero is undefined.

Why is 1 not a suitable logarithmic base?

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.

Why are negative even roots undefined?

Answer: The square root of a negative number is undefined, because anything times itself will give a positive (or zero) result.

Can you have Ln of 0?

Is ln 0 possible?