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Expand log expressions by applying the rules of logarithms. Learn how to break log expressions using product rule into a sum of log expressions. In total, you need at least seven (7) log rules to successfully expand logarithms.
- Logarithm Rules
Rules or Laws of Logarithms. In this lesson, you’ll be...
- Logarithm Explained
Examples of How to Solve Basic Logarithmic Equations....
- Logarithm Rules
This algebra video tutorial explains how to expand logarithmic expressions with square roots using properties of logarithms.
To expand (or break apart) a log expression, apply log rules so that each log contains just one thing. For instance, log(3x²) = log(3) + 2×log(x).
Learn how to expand logarithmic expressions using the product, quotient, and power rules of logarithms. See step-by-step solutions and examples for different types of logarithmic expressions.
Expand a logarithm using a combination of logarithm rules. Condense a logarithmic expression into one logarithm. Expanding Logarithms. 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. For example:
With practice, we can look at a logarithmic expression and expand it mentally, writing the final answer. Remember, however, that we can only do this with products, quotients, powers, and roots—never with addition or subtraction inside the argument of the logarithm.
We can use the properties of the logarithm to expand logarithmic expressions using sums, differences, and coefficients. A logarithmic expression is completely expanded when the properties of the logarithm can no further be applied.
