How to distribute ln into right side of this equation

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In summary, the conversation discusses the use of ln in differentiating a function and how it cannot be distributed like other functions such as cosine or square root. The chain rule is suggested as a method for finding the derivative in this scenario.
  • #1
LearninDaMath
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once i get ln on both sides, I'm then supposed to differentiate both sides...but I won't be able to properly differentiate if ln is not applied.

Does ln get applied to the 976, (-1) and 176t? How?
 
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  • #2
You can use the chain rule here.

Treat 976[ (.835)^t - 1] + 176t as a function of t. Then your equation becomes ln( f(t) ). And you can use the chain rule to determine the derivative.
 
  • #3
To answer the question in your title, you can't "distribute" ln into a sum, because ln is not a factor.

Distributive property: a(b + c) = ab + ac

BUT
cos(b + c) ≠ cos(b) + cos(c)
ln(b + c) ≠ ln(b) + ln(c)
√(b + c) ≠ √b + √c

cos, ln, and √ are functions - there is no distributive property for functions.
 

Related to How to distribute ln into right side of this equation

1. How do I distribute ln into the right side of an equation?

To distribute ln into the right side of an equation, you can use the properties of logarithms. The property states that ln(ab) = ln(a) + ln(b). This means that you can distribute ln into the right side by breaking down the expression into smaller parts and applying the property.

2. Can I distribute ln into both sides of an equation?

Yes, you can distribute ln into both sides of an equation. This is because the property of logarithms mentioned above applies to both sides of an equation, as long as the operations on each side are the same.

3. How does distributing ln change the equation?

Distributing ln into the right side of an equation can change the equation by simplifying it. This is because ln is a logarithmic function that can help simplify exponential expressions. By distributing ln, you can break down the expression into smaller parts that are easier to work with.

4. Are there any restrictions when distributing ln into an equation?

Yes, there are some restrictions when distributing ln into an equation. One restriction is that the expression inside the ln function must be positive. This is because ln is only defined for positive values. Additionally, you cannot distribute ln into an expression with a sum or difference inside the ln function.

5. Can I use other logarithmic functions besides ln?

Yes, you can use other logarithmic functions besides ln to distribute into an equation. Some common logarithmic functions include log (base 10), log (base 2), and log (base e). These functions have their own properties that can be used to distribute them into an equation.

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