how do you expand
Ln abs(�ã(�ã7 x^3+2x^2))
Your �ã symbols do not make sense. Try using parentheses, brackets and "sqrt()" for "square root of ( )"
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To expand the expression Ln |(7x^3 + 2x^2)|, we need to rewrite it in a more simplified and expanded form. Here are the steps to follow:
1. Start by understanding the notation:
- "Ln" represents the natural logarithm function.
- The absolute value symbol "| |" ensures that the argument within it is positive.
2. Expand the expression inside the absolute value:
- The given expression is |(7x^3 + 2x^2)|.
- We can rewrite it as |(x^2) * (7x + 2)|.
3. Notice that the expression inside the absolute value is a product of two terms: x^2 and (7x + 2).
4. Apply the properties of logarithms:
- We know ln(a*b) = ln(a) + ln(b). This property allows us to split the logarithm of a product into a sum of logarithms.
5. Apply the natural logarithm (ln) property:
- ln |(x^2)*(7x + 2)| = ln |x^2| + ln |7x + 2|.
6. Simplify the individual logarithms:
- The natural logarithm of x^2 can be simplified to 2ln|x|.
- The natural logarithm of 7x + 2 remains as ln |7x + 2|.
Therefore, the expanded form of the given expression is 2ln|x| + ln |7x + 2|.