Solving 10^(x+3)=5e^(7-x): Need Help!

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The discussion revolves around solving the equation 10^(x+3) = 5e^(7-x). The user initially attempts to apply logarithms but becomes stuck after rearranging the equation. A helpful response clarifies how to isolate x by moving all x terms to one side and constants to the other. The final solution is presented as x = (ln5 + 7 - 3ln10)/(ln10 + 1). The user expresses gratitude for the assistance in understanding the solution process.
niteshadw
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I'm having a problem with a log question, its rather easy but I'm stuck after certain point.

The question is:

10^(x+3)=5e^(7-x)

I tried solving by:

ln10^(x+3) = ln5 + lne^(7-x)
(x+3)ln10 = ln5 + (7-x)

I am stuck after that, I've tried every combiantion and when I chack it with a calculator answer, my answer is different.

Any help would be much appreciated, thank you.
 
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(x+3)ln10 = ln5 + 7-x that is correct. Now just put all of the x's to the left hand side and all the rest on the other side : xln10 + x = ln5 + 7 - 3ln10

x(ln10 + 1) = ln5 + 7 -3ln10

x = (ln5 + 7 - 3ln10)/(ln10 + 1)

marlon
 
Ah, thank you very much. Your help is much appreciated. I could not fingure out how to get the x's out the correct way. I did not know this was allowed. Thank you again.
 

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