![]() A NEGATIVE PLUS A POSITIVE EQUALS PLUSThe positivity of a number may be emphasized by placing a plus sign before it, e.g. Conversely, a number that is greater than zero is called positive zero is usually ( but not always) thought of as neither positive nor negative. To help tell the difference between a subtraction operation and a negative number, occasionally the negative sign is placed slightly higher than the minus sign (as a superscript). For example, −3 represents a negative quantity with a magnitude of three, and is pronounced "minus three" or "negative three". Negative numbers are usually written with a minus sign in front. For example, −(−3) = 3 because the opposite of an opposite is the original value. The laws of arithmetic for negative numbers ensure that the common-sense idea of an opposite is reflected in arithmetic. Negative numbers are used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. If a quantity, such as the charge on an electron, may have either of two opposite senses, then one may choose to distinguish between those senses-perhaps arbitrarily-as positive and negative. A debt that is owed may be thought of as a negative asset. Negative numbers are often used to represent the magnitude of a loss or deficiency. In the real number system, a negative number is a number that is less than zero. In mathematics, a negative number represents an opposite. So in summary, because the we only allow the log’s base to be a positive number not equal to 1, that means the argument of the logarithm can only be a positive number.This thermometer is indicating a negative Fahrenheit temperature (−4 ☏). Then what we know is that, if the base of our power function is positive, it doesn’t matter what exponent we put on that base (it could be a positive number, a negative number, or 0), that power function is going to come out as a positive number. 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.įor that reason, we only allow positive numbers other than 1 as the base of the logarithm. So 0, 1, and every negative number presents a potential problem as the base of a power function. And as you know, unless we’re getting into imaginary numbers, we can’t deal with a negative number underneath a square root. If you raise a negative number to a positive number that’s not an integer, but instead a fraction or a decimal, you might end up with a negative number underneath a square root. In the same way, 1 raised to anything is always still 1. Or, put a different way, 0 raised to anything is always still 0. In other words, there’s no exponent you can put on 0 that won’t give you back a value of 0. When you have a power function with base 0, the result of that power function is always going to be 0. To understand why, we have to understand that logarithms are actually like exponents: the base of a logarithm is also the base of a power function. The reason has more to do with the base of the logarithm than with the argument of the logarithm. Negative numbers, and the number 0, aren’t acceptable arguments to plug into a logarithm, but why? In other words, the only numbers you can plug into a log function are positive numbers. The argument of a log function can only take positive arguments. While the value of a logarithm itself can be positive or negative, the base of the log function and the argument of the log function are a different story. ![]()
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