## anonymous 5 years ago e^x4=1000

1. anonymous

to cancel out e you have to take the ln to both sides$\ln( e ^{(4*x)})=ln(1000)$ ${(4*x)}=ln(1000)$ ${(x)}=(ln(1000))/4$

2. anonymous

I thought I had to 4th root each side because I am left with x^4=ln1000?

3. anonymous

Am I wrong?

4. anonymous

its xto the 4th not 4*x?

5. anonymous

What is the original equation? a) $$e^{x^4} = 1000$$ b) $$e^{x4} = 1000$$ c) $$e{x^4} = 1000$$

6. anonymous

a

7. anonymous

Ok, so start by taking the natural log of both sides.

8. anonymous

You can't take the 4th root yet because you'd have $(e^{x^4})^{\frac{1}{4}} = e^{\frac{x^4}{4}}$

9. anonymous

$e ^{x ^{4}} = 1000$ so $ln(e ^{x ^{4})} = ln(1000)$ ${x ^{4}} = ln(1000)$ $x= \sqrt[4]{\ln(1000)}$ or you can say $x= (\ln(1000))^{1/4}$

10. anonymous

It wouldn't get rid of the power of 4 on the x.

11. anonymous

Is there an answer to this or is that it?? I am so confused?

12. anonymous

Romero is correct. The answer is the $x=\sqrt[4]{ln\ 1000}$

13. anonymous

do I type that into my caculator to get an answer??

14. anonymous

sure, or you can leave it that way.

15. anonymous

What would the answer be if I typed it into my caculator. I am new to this scientific....is it 10.5130????

16. anonymous

I have 1.6211

17. anonymous

err 1.62119 rather.

18. anonymous

Thank you.. with that answer I was able to figure out which buttons to press on this caculator... its going to be the death of me...!!