Rewriting Ln function and getting a wrong function?

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    Function Ln
In summary, the conversation discusses the error in rewriting a potens function and the correct way to raise the right side of an equation to e. The mistake lies in assuming that e^{x+y}=e^x+e^y, when in fact it should be e^{x+y}=e^x e^y. Several people have previously explained this error to the person in question.
  • #1
christian0710
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This is really strange: If i rewrite a potens function i get a function which should not be possible (it does not give the same values). What did i do wrong?

Y = b*X^a
lnY = ln(b*X^a)
lny = lnb + ln X^a
lnY = lnb + a*lnx

we raise both sides to e

Y = b+ e^(a*lnx)=b+( e^lnx)^a = b + X^a

I think b+ x^a is very diffrent that b*x^a ?
 
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  • #2
The point is, [itex] e^{x+y}=e^x e^y [/itex] but you assumed [itex] e^{x+y}=e^x+e^y [/itex] which is wrong!
 
  • #3
Shyan said:
The point is, [itex] e^{x+y}=e^x e^y [/itex] but you assumed [itex] e^{x+y}=e^x+e^y [/itex] which is wrong!

So are you saying that when i raise the right side of an equation (lnb + a*lnx ) to e, I should raise it like this e^(lnb + a*lnx ) and not the individual terms?
 
  • #5
That's exactly what you used when you went from ln(ab) to ln(a)+ ln(b).
 
  • #6
christian0710 said:
This is really strange: If i rewrite a potens function i get a function which should not be possible (it does not give the same values). What did i do wrong?

Y = b*X^a
lnY = ln(b*X^a)
lny = lnb + ln X^a
lnY = lnb + a*lnx

we raise both sides to e

Y = b+ e^(a*lnx)=b+( e^lnx)^a = b + X^a

I think b+ x^a is very diffrent that b*x^a ?

You made the same basic error in another thread, and in that thread several people explained to you where your mistake lies. Please pay attention to what people are explaining to you!
 

1. What is the purpose of rewriting the Ln function?

The natural logarithm (Ln) function is commonly used in mathematics and science to solve problems involving exponential growth or decay. Rewriting the Ln function allows us to manipulate and simplify the function for easier calculations or to find new relationships between variables.

2. How do you rewrite the Ln function?

The Ln function can be rewritten using logarithm rules, such as the power rule, product rule, or quotient rule. These rules allow us to manipulate the arguments of the Ln function to simplify the expression or find a different representation of the function.

3. Is rewriting the Ln function always necessary?

No, rewriting the Ln function is not always necessary. In some cases, the original form of the function may be more useful or appropriate for the problem at hand. However, in complex calculations or when trying to find new relationships between variables, rewriting the Ln function can be beneficial.

4. Why might a rewritten Ln function result in a wrong function?

Rewriting the Ln function involves applying logarithm rules, which may introduce errors if not applied correctly. Additionally, the rewritten function may not accurately represent the original function if certain assumptions or restrictions are not taken into account.

5. How can you check if a rewritten Ln function is correct?

To check if a rewritten Ln function is correct, you can use a graphing calculator or software to graph both the original and rewritten functions and compare them. You can also plug in specific values for the variable and see if the output matches the original function. It is also helpful to double-check the steps used in the rewriting process to ensure no errors were made.

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