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

[niteshadw]

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.

 

[marlon]

(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

 

[niteshadw]

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.