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

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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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