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What's wrong with my calculations?
I feel I must be doing something really stupid, but I cannot figure out what!
I want to solve this equation for x...
10^(x+3) = 5e^(7-x)
To figure it out I divided by five and then took the natural log of both sides, etc.
I get the answer 2.9, but if I put that back into the original equation, I get an inequality.
Wolfram says the answer is 0.515... which works if you put it back into the initial equation, but I have no idea how they got that answer!
Someone please tell me how to solve this correctly because it's driving me crazy.
I feel like an idiot... You guys are absolutely awesome. Thank you. :)
2 Answers
- IronboxyLv 610 years agoFavorite Answer
ln[10^(x + 3)] = ln[5e^(7 - x)]
(x + 3)(ln10) = ln5 + ln(e^(7 - x))
(x + 3)(ln10) = ln5 + (7 - x)(ln(e))
(x + 3)(ln10) = ln5 + (7 - x)(1)
xln10 + 3ln10 = ln5 + 7 - x
xln10 + x = ln5 - 3ln10 + 7
x(ln10 + 1) = ln5 - 3ln10 + 7
x = [ln5 - 3ln10 + 7] / [ln10 + 1]
x = 0.515....
Hope this helps :D
Why did you, and how did you divide by 5 on both sides? there's no "constant" infront of the 10.
It's alright, we all make mistakes :D
- 10 years ago
e^((x + 3)ln(10)) = 5e^(7 - x)
e^((x + 3)ln(10) + x - 7) = 5
(x + 3)ln(10) + x - 7 = ln(5)
[ln(10) + 1]*x + 3âln(10) - 7 = ln(5)
[ln(10) + 1]*x = ln(5) - 3âln(10) + 7
x = [ln(5) - 3âln(10) + 7] / [ln(10) + 1] â 0.51526
