Ackbach said:What have you tried?
[tex]\text{Simplify: }\:\tfrac{1}{5}\ln|\sin5x|+\tfrac{1}{5}\ln|\csc5x-\cot5x|[/tex]
soroban said:Hello, paulmdrdo!
[tex]\begin{array}{ccc}\text{Factor:} & \tfrac{1}{5}\big(\ln|\sin5x| + \ln|\csc5x - \cot5x|\big) \\ \\ \text{Combine logs:} & \tfrac{1}{5}\ln|\sin5x(\csc5x - \cot5x)| \\ \\ \text{Distribute:} & \tfrac{1}{5}\ln|\sin5x\csc5x - \sin5x\cot5x| \\ \\ \text{Simplify:} & \tfrac{1}{5}\ln|1-\cos5x| \\ \\ \text{Further?} & \tfrac{1}{5}\ln\left|2\sin^2\! \tfrac{5x}{2}\right| \end{array}[/tex]
Simplification of expression is a mathematical process of reducing an algebraic expression into a simpler form by combining like terms and using properties of operations.
Simplifying expressions allows for easier computation and understanding of mathematical equations. It also helps to identify patterns and relationships between different terms.
To simplify an algebraic expression, you need to combine like terms by adding or subtracting coefficients, and using properties of operations such as the distributive property, commutative property, and associative property.
Yes, for example, the expression 3x + 2x can be simplified to 5x by combining the like terms 3x and 2x. Similarly, the expression 4(3x + 2) can be simplified to 12x + 8 by using the distributive property.
Some common mistakes to avoid when simplifying expressions include forgetting to combine like terms, not applying the correct properties of operations, and making calculation errors. It is important to double-check your work and use proper notation to avoid mistakes.