Using Logs to Expand an Expression
On the board log(xy) should not have base a since it was not written for the rest of the equation.
Also, ln x³(x² + 3 )^(1/4) should be written as ln [x³(x² + 3)]^(1/4). Only then x³ will also be raised to the power of 1/4.
In this lesson, you will learn how to use the properties of logarithms to expand an expression with roots. The first step is to rewrite the expression using natural logs, and then apply the log property to bring the root to the front. Next, you can expand the multiplication inside the brackets and simplify. Finally, you can bring the exponents outside the brackets and rearrange the terms. By following these steps, you can confidently use properties of logs or natural log to expand any expression.
How to use properties of logs to expand an expression with roots
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- How are Natural logarithms written?
- What is log xâµ equal to ?
- What can you say about the laws of Natural Logarithms?
- Based on the above example and using the Laws of Natural Logarithms rewrite lnâ(x²(x³ +2))
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Staff Review
A challenging example to attempt as it incoperates more than one law.
