anonymous 5 years ago i need help solving logarithmic equations

1. anonymous

$\log_{5} 4-\log_{5} 3r=3\log_{5} 2$

2. anonymous

you want to find r? ^_^

3. anonymous

yes.

4. anonymous

but i need step by step help so i can understand it.

5. anonymous

Alright, here we go :) :$-\log_{5}3r = \log_{5}2^3 - \log_{5}4$$\log_{5}3r = -\log_{5}2^3 +\log_{5}4$$\log_{5}3r = \log_{5}(8.4)$$\log_{5}3r = \log_{5}32$$\log_{5}3r = 2.15 \rightarrow 3r = 5^{2.15} \rightarrow r = \frac{5^{2.15}}{3} \approx10.6$ correct me if I'm wrong please ^_^

6. anonymous

i'm not sure if it's right or wrong. that's my problem. i have no knowledge on this at all.

7. anonymous

hmm , alright the basic rules : $\log_{b}n + \log_{b}k = \log_{b}(n + k)$ $\log_{b}n -\log_{b}k = \log_{b}(\frac{n}{k})$ I think I've done a silly mistake lol , hold on :)

8. anonymous

Use the properties of logerithms: $\log _{5}4-\log _{5}3r=\log _{5}[4/(3r)]$ Also $3\log _{5}2=3\log _{5}2^3=3\log _{5}8$ $\log _{5} [4/(3r)]=\log _{5}8$ 4/3r=8 So r=1/6

9. anonymous

=// after the Also ignore the 3s after the equal signs

10. anonymous

this step :$\log_{5} 3r = \log_{5}4 - \log_{5} 8$ must be : $\log_{5}3r = \log_{5} \frac{4}{8}$

11. anonymous

you can take it up from here, right? :) I think xav's answer is correct since I did a silly mistake lol, sorry ^_^"

12. anonymous

r=1/6

13. anonymous

Thats correct

14. anonymous

Thank you so much :)

15. anonymous

alright , so xav's + iam's answer = correct dear ^_^, did you understand the concept now?

16. anonymous

alright , so xav's + iam's answer = correct dear ^_^, did you understand the concept now?

17. anonymous

Well, you can verify if the answer is correct or not by going here http://www.wolframalpha.com/input/?i=log5%284%29%E2%88%92log5%283r%29%3D3log5%282%29

18. anonymous

Yes i did. I have plenty more problems i need help with. Can anyone be patient with me and help me through all of them ? :)

19. anonymous

20. anonymous

21. anonymous

$\log_{2} 4-\log_{2} (x+3)-\log_{2} 8$

22. anonymous

What do you want to do with this

23. anonymous

Simplify ?

24. anonymous

I guess solve for x

25. anonymous

Wait... >_<

26. anonymous

Where is the =

27. anonymous

No. all the problems i'm posting are solving each equation.

28. anonymous

Where is the =

29. anonymous

oh wait i see what you saying the = is supposed to be after (x+3)

30. anonymous

okay

31. anonymous

$2-log2(x+3)=3$

32. anonymous

Where 2 is at the base

33. anonymous

yes 2 is the base.

34. anonymous

But that leads to no solution

35. anonymous

36. anonymous

$\log_{2} 4-\log_{2} 8=\log_{2} (x+3)$

37. anonymous

We can write (4/8)=x+3

38. anonymous

The rest you can do