## anonymous 5 years ago I need someone to just check my work... and tell me where I went wrong?

1. anonymous

The problem is 2^x+3=5x

2. anonymous

What did you get?

3. anonymous

next step: (x+3)ln2/xln2=xln5/xln2

4. anonymous

I got 2.269

5. anonymous

next step: x+3/x=ln5/ln2

6. anonymous

next step: x+3/x=2.322/1

7. anonymous

Something is wrong. Was the original equation $2^{x+3} = 5^x$ ?

8. anonymous

no 2^ x+3=5x

9. anonymous

Ok, then when you take the ln of both sides you'll have ln5 + lnx on the right hand side of the equal.

10. anonymous

Which is gonna be a pain.

11. anonymous

Was it $2^{x+3} = 5x$ ?

12. anonymous

Yes

13. anonymous

Yeah, there's no good way to simplify that. I suspect you have the question wrong.

14. anonymous

Best you can do is something like $x(ln 2) - lnx = ln(5/3)$

15. anonymous

Err wait, that should be ln(5/8) on the right side.

16. anonymous

My teacher told us to set each side to the natural... which gave me: (x+3)ln2=xln5

17. anonymous

Then I needed to get everything canceled out by cross multiplying... so I divided both sides by xln2

18. anonymous

That's not right though. Unless you had 5^x on the right side originally.

19. anonymous

Was it $$5x$$ or $$5^x$$

20. anonymous

the second one... I just looked in my book. Im so sorry

21. anonymous

Ok good.

22. anonymous

So yeah that's right. take the ln of both sides (or any log really)

23. anonymous

Then solve for x. Don't plug anything into your calculator until you have something where x = something that has no x

24. anonymous

(x+3)ln2=xln5 is correct for starting out

25. anonymous

ok... then what do I need to divide both sides by? she taught us to cross multiply? I divided both sides by xln2 just to cancel out. And I ended up with x+3/x=ln5/ln2

26. anonymous

Get all terms with an x on one side.

27. anonymous

Or that. Cross multiplying works fine

28. anonymous

I usually multiply out products, but you don't need to here

29. anonymous

Just be sure that you do (x+3)/x = ln5/ln2

30. anonymous

Not just the 3.

31. anonymous

I did and I got: x+3/x= 2.322/1

32. anonymous

then: x+3=2.322x

33. anonymous

Don't plug things in.

34. anonymous

Keep solving the equation until you have x by itself. x = something that has no x.

35. anonymous

Then plug in

36. anonymous

Im not sure what/where.I am attempting to get x by itself? I thought that is what I was doing?

37. anonymous

I think cross multiplying is just making this harder.

38. anonymous

I just got a different answer of -4.425

39. anonymous

Lets back up.

40. anonymous

Ok..Im just trying to follow the instructions. But Im willing to try anything at this point

41. anonymous

$(x+3)ln2=xln5$ $x(ln2)+3(ln2)=x(ln5)$ $x(ln2)- x(ln5)= - 3(ln2)$ $x[(ln2)- (ln5)]= - 3(ln2)$ $x= \frac{- 3(ln2)}{(ln2)- (ln5)}$

42. anonymous

Thanks for your time.. I appreciate it. I will continue to search for the answer. I need to learn it the way she taught us, Im afraid I will be jumping the gun and not learning anything... thanks so much.