## anonymous 4 years ago solve by creating same bases: 1/9 = 27 ^ x-1

1. Mertsj

$\frac{1}{9}=3^{-2}$

2. Mertsj

$27^{x-1}=(3^{3})^{x-1}$

3. Mertsj

$(3^{3})^{x-1}=3^{3x-3}$

4. Mertsj

So:$3^{-2}=3^{3x-3}$

5. Mertsj

And -2=3x-3 1=3x 1/3=x

6. anonymous

7. Mertsj

Post it.

8. anonymous

properties of logarithms: 3^x=5^x+2

9. anonymous

3^x=5^(x+2)

10. Mertsj

$x \log_{10}3=(x+2)\log_{10}5$

11. anonymous

How did you get that?

12. Mertsj

Find the log of 3 and the log of 5 using your calculator and solve the equation.

13. Mertsj

$a ^{n}=n \log_{10}a$

14. anonymous

how did you know what the variables were?

15. Mertsj

That is the property of law of logs. Perhaps your book uses different variables. What the variables are doesn't matter. Did you book say: $m ^{n}=n \log_{10}m$

16. anonymous

oh eyes!

17. anonymous

yes

18. Mertsj

So use that property on 3^x

19. Mertsj

Would you not get xlog3?

20. anonymous

I think my answer is wrong :/

21. Mertsj

What did you get?

22. anonymous

4.52

23. Mertsj

Hang on.

24. Mertsj

xlog3=.477x and (x+2)log 5 = .699x+1.40

25. Mertsj

do you agree with that/

26. anonymous

Yes!

27. Mertsj

Subtract .699x from both sides.

28. Mertsj

-.222x=1.40

29. anonymous

Oh so the final answer is 1.40?

30. Mertsj

Now divide both sides by -.222

31. anonymous

Oh so -6.31?

32. Mertsj

yes.

33. anonymous

THANK YOU SO MUCH! seriously, you are my life-saver. Now I have one more, I don't want to make you have to show me but could I just ask you a question about it?

34. Mertsj

Yes

35. anonymous
36. anonymous

I don't get if there's acertain equation I am supposed to apply because it looks so confusing.

37. Mertsj

This involves two laws of logs. On the left side you have the difference of two logs which is equal to the log of the quotient.

38. Mertsj

$\log_{3} \frac{x+1}{x}$

39. Mertsj

The right side is the property we used in the last problem.

40. Mertsj

$2\log_{3}2=\log_{3}2^{2}$

41. Mertsj

So now, if the logs are equal, and the bases are the same, the arguments must be equal

42. Mertsj

$\frac{x+1}{x}=2^{2}$

43. Mertsj

solve that equation.

44. Mertsj

Cross multiply

45. Mertsj

4x=x+1

46. Mertsj

3x=1 x=1/3

47. anonymous

thank you so so so much!