The base b logarithm of a number is the exponent that we need to raise the base in order to get the number. The logarithm of the multiplication of x and y is the sum of logarithm of x and logarithm of y. The logarithm of the division of x and y is the difference of …

“The logarithm of a positive real number a with respect to base b, a positive real number not equal to 1 [nb 1], is the exponent by which b must be raised to yield a”. i.e. by= a ⇔logba=y. Where, “b” is called the base, which is at the bottom of the log.

Learn the eight (8) log rules or laws to help you evaluate, expand, condense, and solve logarithmic equations. Try out the log rules practice problems for an even better understanding.

On a calculator it is the "log" button. It is how many times we need to use 10 in a multiplication, to get our desired number. Another base that is often used is e (Euler's Number) which is about 2.71828. This is called a "natural logarithm".

6 days ago · Formula: log a (a) = 1. Example: log 7 (7) = 1. Reciprocal Rule. According to the reciprocal rule of logarithms, the logarithm of a number’s reciprocal (1 divided by that number) is equal to the negative of the logarithm of the original number. In mathematical notation: Formula: log a (1/X) = – log a (X) Example: log a (1/2) = – log a (2)

Feb 11, 2025 · logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = log b n. For example, 2 3 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log 2 8. In the same fashion, since 10 2 = 100, then 2 = log 10 100.

Log a a. Since a 1 = a, for any 'a', converting this equation into log form, log a a = 1. Thus, the logarithm of any number to the same base is always 1. For example: log 2 2 = 1; log 3 3 = 1; log 10 = 1; ln e = 1; Product Rule of Log. The logarithm of a product of two numbers is the sum of the logarithms of the individual numbers, i.e., log a ...