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)
The pre-exponential factor, or frequency factor, is an aspect of the Arrhenius equation and is related to collision theory. The value for this factor varies depending on the chemical reaction and is determined through experimental observation. However, if values of the rate constant, k, are known at
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
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.
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.
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.
Logarithmic differentiation refers to the process in calculus of finding the derivative of a function by using the properties of the natural logarithmic function. The natural logarithmic function is notated by "ln."
To graph a logarithmic function, the domain of the function is determined, which is a set of all allowable x values. The domain is used to calculate a range of y values. The vertical asymptote gives the value near which the function changes rapidly. The x and y intercepts are calculated. Using all t
Some information on logarithms that may be included in an algebra 2 course include the relationship between logarithms and exponents and the relationship between the natural logarithm and the constant e. Other material may cover the basic properties of a logarithm, such as subtraction and division.