In the next examples, we will solve some problems involving pH. Taken together, the product rule, quotient rule, and power rule are often called “properties of logs.” Sometimes we apply more than one rule in order to expand an expression. Condense a logarithmic expression into one logarithm.These rules are typically listed in algebra or pre-calculus. The logarithm of a product rule indicates that the multiplication of two or more logarithms with the. To expand or condense logarithms we need to know and be able to apply special logarithmic rules. Here, we will learn about the properties and laws of logarithms. When condensing logarithms we use the rules of logarithms, including the. Expand a logarithm using a combination of logarithm rules. The properties of logarithms, also known as the laws of logarithms, are useful as they allow us to expand, condense, or solve equations that contain logarithmic expressions. Algebra Logarithmic Expressions and Equations Simplify/Condense ln (x) + ln(yx).Write the equivalent expression by multiplying the exponent times the logarithm of the base.Express the argument as a power, if needed.To use the power rule of logarithms to write an equivalent product of a factor and a logarithm, consider the following: Rule 2: Quotient Rule The logarithm of the quotient of numbers is the difference of the logarithm of individual numbers. If not, apply the product rule for logarithms to expand completely. Descriptions of Logarithm Rules Rule1: Product Rule The logarithm of the product of numbers is the sum of the logarithms of individual numbers. We will learn later how to change the base of any logarithm before condensing. For our purposes in this section, condensing a multiple of a logarithm means writing it as another single logarithm. ![]() ![]() It is important to remember that the logarithms must have the same base to be combined.
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