Why do logarithms have to be positive?

When you have a power function with base 0, the result of that power function is always going to be 0. 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.

Can logarithms answer negative?

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.

Why can’t LN be negative?

The natural logarithm function ln(x) is defined only for x>0. So the natural logarithm of a negative number is undefined. The complex logarithmic function Log(z) is defined for negative numbers too.

What should logarithms always equal?

0
The logarithm of 1 always equals 0. Any number can serve as b, the base.

What are the mantissa and the characteristics of a logarithm?

The integral part of a common logarithm is called the characteristic and the non-negative decimal part is called the mantissa. Suppose, log 39.2 = 1.5933, then 1 is the characteristic and 5933 is the mantissa of the logarithm.

What is the mantissa in a floating-point?

The mantissa represents the actual binary digits of the floating-point number. The power of two is represented by the exponent. The stored form of the exponent is an 8-bit value from 0 to 255.

Can a log base be a fraction?

Yes, of course.

What is the quotient rule for logarithms?

The quotient rule for logarithms says that the logarithm of a quotient is equal to a difference of logarithms. Just as with the product rule, we can use the inverse property to derive the quotient rule.

What is the relationship between logarithms and exponentials?

Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = ax is x = ay. The logarithmic function y = logax is defined to be equivalent to the exponential equation x = ay.

What is the mantissa of a logarithm?

The integral part of a logarithm is called the characteristic and the fractional part (decimal part) is called mantissa. i.e., log N = Integer + Fractional or decimal part (+ve) ⇒ The mantissa of the log of a number is always kept positive.

What is the characteristic of the logarithm of a number?

1. The characteristic of the logarithm of a number must be an integer, negative or positive 2. the Mantissa of the logarithm of a number must be a positive proper fraction. from the two examples above, what is the relation between the number of zeroes to the right of the decimal in the number on the left and the negative integer on the right.

How do you know if the logarithm is positive or negative?

If the number x and the base ‘a’ are on the same side of the unity, then the logarithm is positive. If the number x and the base a are on the opposite sides of the unity, then the logarithm is negative. 3. Graph of

What is the logarithm of B to the base a?

The logarithm of any positive number, whose base is a number, which is greater than zero and not equal to one, is the index or the power to which the base must be raised in order to obtain the given number. = 1), then x is called the logarithm of b to the base a and we write log a b = x, clearly b > 0. Thus = 1 and b > 0.