## pratu043 Group Title Can someone please explain how to solve a log equation with an example. 2 years ago 2 years ago

1. dpaInc Group Title

how 'bout u pick an example....

2. dpaInc Group Title

otherwise i'll choose the easiest...:)

3. pratu043 Group Title

OK ... $5^{x - 3} . 3^{2x-8} = 225$

4. pratu043 Group Title

How to solve this using log? I'm new so I have no idea.

5. pratu043 Group Title

I mean new to log.

6. pratu043 Group Title

pls help.

7. lgbasallote Group Title

welcome to logarithms!

8. pratu043 Group Title

Yeah thanks!

9. waterineyes Group Title

I guess you can solve this without using Logs..

10. pratu043 Group Title

But I want to know how to do it with log.

11. waterineyes Group Title

Okay then all here will explain you how to do this...

12. moha_10 Group Title

15^(x-3)+(2x-8)=225 now we take ln (3x-11)15= ln225

13. pratu043 Group Title

What is In? And how did you get 15^(x-3)+(2x-8)=225?

14. moha_10 Group Title

15*ln(3x-11)=ln 225

15. moha_10 Group Title

by multi 3 into 5 to get 15 and the exponent it's added

16. pratu043 Group Title

But how can you just multiply the base and add the exponents?

17. waterineyes Group Title

Use the following formulas of Logs: $\large Log(a \times b) = Log(a) + Log(b)$ $\large Log(a)^b = b.Log(a)$

18. moha_10 Group Title

before we take the logarithem

19. moha_10 Group Title

it's from exponent experepties

20. pratu043 Group Title

Why did you delete that @dpaInc?

21. dpaInc Group Title

because i don't wanna take away from these guys awesome explanations....:)

22. waterineyes Group Title

See, take Log both the sides you will get: $\large Log(5^{x-3}.3^{2x-8}) = Log(225)$ Now use the formulas I have written above..

23. waterineyes Group Title

Use the first formula only...

24. pratu043 Group Title

$\log(5^{x-3}) . \log(3^{2x-8}) = \log 225$

25. waterineyes Group Title

Now Check my first formula carefully...

26. moha_10 Group Title

27. moha_10 Group Title

like what waterineyes did now

28. pratu043 Group Title

That's what I've done here right @waterineyes?

29. waterineyes Group Title

I give you an example: $\large Log(2 \times 3) = Log(2) + Log(3)$ Go by this procedure...

30. pratu043 Group Title

I've already done that. So now we should use the second one?

31. waterineyes Group Title

You have done it wrongly my friend...

32. waterineyes Group Title

See check the formula.. After formula the result will be in sum form and your result is not in sum form.. Is there any + sign in your result???

33. pratu043 Group Title

Oops. $\log(5^{x-3}) + \log(3^{2x-8}) = \log225$

34. waterineyes Group Title

Yes now you are right... Now 225 is square of what number???

35. pratu043 Group Title

15

36. waterineyes Group Title

So can you write 225 as $$15^2$$ on right hand side.?? If yes then do it..

37. pratu043 Group Title

$\log(5^{x-3}) + \log(3^{2x-8}) = \log15^{2}$

38. waterineyes Group Title

Now use the power rule of Logarithms that is the Second Formula that I have given above.. Can you use that??

39. waterineyes Group Title

I give you an example of that too: $\large Log(x)^4 = 4.Log(x)$

40. pratu043 Group Title

$(x-3)\log5 + (2x-8)\log3 = 2\log15$

41. waterineyes Group Title

Can you write 15 as 3*5??

42. pratu043 Group Title

Yes. $(x-3)\log5 + (2x-8)\log3 = 2\log(5 * 3)$

43. waterineyes Group Title

Then use it and use the first formula again on right hand side...

44. pratu043 Group Title

$(x-3)\log5 + (2x-8)\log3 = 2\log5 + 2\log3$

45. waterineyes Group Title

Now what you have to do is to compare the coefficients of $$Log3$$ and $$Log5$$ both the sides can you do that??

46. waterineyes Group Title

Tell me the coefficient of Log3 on Left hand side and right hand side...

47. pratu043 Group Title

On LHS its 2x - 8 and on RHS its 2.

48. waterineyes Group Title

Just equate them and find x from it..

49. waterineyes Group Title

Similarly equate the coefficients of log5 and then also find x you will get the same x in both the case...

50. waterineyes Group Title

No no...

51. pratu043 Group Title

$(2x-8)\log3 = 2\log3$

52. waterineyes Group Title

I said to equate the coefficients buddy.. Coefficients are 2x - 8 and 2.. you should equate this only...

53. pratu043 Group Title

So you should just do 2x-8 = 2?

54. pratu043 Group Title

x = 5

55. waterineyes Group Title

See, if : $\large xlog3 = ylog3$ implies x = y. Getting??

56. pratu043 Group Title

Yes!!

57. waterineyes Group Title

Yes you have found x = 5 that is absolutely right...

58. pratu043 Group Title

Thanks a lot!!

59. waterineyes Group Title

Now equate the coefficients of log5..

60. pratu043 Group Title

x - 3 = 2 x = 2 + 3 = 5

61. waterineyes Group Title

Yes got the same value of x so you are right.. If anyhow x values are coming different then either question is wrong or your solution is wrong.. Getting??