Logarithms follow very similar rules and procedures as exponents. They follow a Product, Power, and Quotient Rule. The Product Rule tells us that the log of a product is equal to the sum of log of the first and second base. The log of a quotient is the difference of the logs of numerator and denominator. The Power Rule is used when we are looking for the log of a power. The log of any power is equal to the product of the power and the log of the base. There is also a formula for when we are changing bases. It states that the log of a new is the long of the old divided by the new base.
Logarithmic and exponential forms are an important aspect of mathematics. Since they are the core concepts used to calculate the magnitude intensity of an earthquake. For instance, you can compare the magnitudes of two earthquakes, by converting between logarithmic and exponential form. Let us take an example to improve our understanding. The amount of energy released from the first earthquake was 400 times greater than the energy released from the other. The equation that represents this is the problem is 10y = 400, where y is the difference in magnitude showed on the Richter scale. We have to solve for y. Now, there are many ways to convert them. The first is by using graphs. However, estimating from graphs can may give you an approximate answer. Thus, we use a log to convert the above exponential function in a logarithmic function. Let's find out practically. First, we have to learn the values of b, and y, to write the equation in log form. The b is the base for log form, while y is the unknown variable of the function. In the present example 10y = 500, The value of b is 2; thus the answer becomes, log10 500 = x. These worksheets explain how to convert logarithmic expressions into exponential form. Though the formulas have been provided, students should already be familiar with the material.