Solve 7x ln(5) = 10x ln(7) Confusion

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Homework Help Overview

The discussion revolves around solving the equation 7x ln(5) = 10x ln(7) and clarifying the interpretation of the expression 5e^(7x). Participants are exploring the implications of different interpretations of the expression within the context of logarithmic properties.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the interpretation of the expression 5e^(7x) and whether it should be treated as 5*(e^(7x)) or (5e)^(7x). There is also confusion regarding the role of the natural logarithm and how it applies to the components of the equation.

Discussion Status

The discussion is ongoing, with participants actively questioning assumptions and interpretations. Some have provided insights into the differences in handling the logarithmic expressions, but there is no explicit consensus on the correct approach yet.

Contextual Notes

Participants are grappling with the implications of their interpretations and the potential impact on the problem-solving process. There is a noted confusion about whether the constant 5 is included in the natural logarithm and how that affects the equation.

IntegrateMe
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5e^(7x) = 7e^(10x) ??

7x ln(5e) = 10x ln(7e)

7x * (ln5 + ln e) = 10x * (ln7 + ln e)

7x * (ln5) = 10x * (ln7)

Now I have nowhere to go. What am I doing wrong?
 
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5e^(7x) probably means 5*(e^(7x)) not (5e)^(7x) as you are treating it.
 


How does that make a difference?
 


IntegrateMe said:
How does that make a difference?

All the difference in the world. Try it.
 


5*7x ln e = 7 * 10 ln e

35x = 70x?

This doesn't seem right. Can you please explain how I would start this? Is the 5 included in the natural log?
 


IntegrateMe said:
5*7x ln e = 7 * 10 ln e

35x = 70x?

This doesn't seem right. Can you please explain how I would start this? Is the 5 included in the natural log?

ln(5*e^(7x))=ln(5)+ln(e^(7x)). It's looking different already, isn't it? Not the same as ln((5e)^(7x))=7x*ln(5e).
 


Thank you!
 

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