Logarthims of the same base can be added together by multiplying their arguments and then performing the logarithm on the product. For example, assuming log means log base 10 as it does on a calculator: log(x) + log(y) = log(x * y)
An exponent is a shorthand way of showing how many times to multiply a number by itself. The number 9 with a small raised 3 on its upper right, also commonly expressed as 9^3, represents the base of 9 to the 3rd power, for instance; the raised 3 is the exponent. Simplify multiplication of two expone
Because they are so closely related to exponential functions, logarithms have a number of applications in real life, especially when calculating the pH of any chemical substance or measuring the loudness of sounds through the use of decibels. Both of these activities, common in many different indust
The power property of logarithms states that any exponent in the argument of a logarithmic function can be brought out as a multiplier to the rest of the expression. In algebraic form (note that ? is used to denote a logarithmic base): log?b(x^c) = c * log?b(x) Assuming that log means log with base
When two logarithms of the same base are subtracted, the arguments of each logarithm are divided. For example, if two logarithms of base 10 with arguments of 10 and 2 are subtracted, the expression is resolved to a single logarithm of base 10 with an argument of 5.
The Greek mathematician Archimedes is credited with discovering and proving the law of exponents in "The Sand Reckoner." His famous work was designed to express the number of grains of sand that can fit in the universe, leading to a discussion about the way to refer to large numbers.
Using known properties of logarithms, one can expand a complex logarithmic expression into a series of simpler expressions. Logarithmic expressions are abbreviated with log and may involve combinations of multiplication, division and exponents.
In order to multiply logarithms with different bases, the change of base formula must be used. The change of base formula is log_b_a = (log_c_a) / (log_c_b). The easiest way to use the change of base formula is to change the bases to base 10.
An exponent tells the problem solver how many times to multiply a number by itself; therefore, a zero exponent tells the problem solver to multiply the number zero times by itself. Basically, any number with a zero exponent is equal to one, unless the base number is zero.
Exponents are numbers that indicate the number of times a function is multiplied by itself, while logs are used to determine the exponential function needed to express a particular number or mathematical phrase. Exponents can be expressed through log functions, and logs can be expressed through expo