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anonymous

  • 5 years ago

I have a logarithmic problem solve for x approximate 4^(x+4)=5^(x-6)

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  1. anonymous
    • 5 years ago
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    take logs both sides ( doesnt matter what base, as long as they are the same )

  2. anonymous
    • 5 years ago
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    ill use base e

  3. anonymous
    • 5 years ago
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    take log on both side, then you'll get (x+4)log 4 = (x-6)log 5, solve it and get the answer.

  4. anonymous
    • 5 years ago
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    ln [ 4^(x+4) ] = ln [ 5^(x-6) ] now use log laws to bring power down in front

  5. anonymous
    • 5 years ago
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    etc ...

  6. anonymous
    • 5 years ago
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    I don't come up with the correct answer I have had it wrong 5 times

  7. anonymous
    • 5 years ago
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    I have 4 log 5+4log5 / log5-log 4 how do I solve it with the calculator they come up with an approximate

  8. anonymous
    • 5 years ago
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    I don't have my calculator right now with me, nor my internet connection is working fine and this site is damn slow or else i would have solved that for you.

  9. anonymous
    • 5 years ago
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    how do you solve it

  10. anonymous
    • 5 years ago
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    it's roughly 68.1257..

  11. anonymous
    • 5 years ago
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    how did you get that

  12. anonymous
    • 5 years ago
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    I have another one you might be able to help me with use log b 2=0.693 and /or lo b 7 =1.946 to find log b 14

  13. anonymous
    • 5 years ago
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    the b is below log

  14. anonymous
    • 5 years ago
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    you have to get an approximate also

  15. anonymous
    • 5 years ago
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    don't have any clue how to do it no examples

  16. anonymous
    • 5 years ago
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    I only come on when I am stuck on problems

  17. anonymous
    • 5 years ago
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    \[4^{x+4} = 5^{x-6}\] \[(x+4)\log4 = (x-6)\log6 \] \[x \log(4)+4 \log(4) = x \log(5) - 6 \log (5)\] \[x \log (4) - x \log (5) = -6 \log (5) - 4 \log (4)\] \[x(\log(4)-\log(5)) = -6 \log (5) - 4 \log (4)\] \[x = {{-6 \log (5) - 4 \log (4)} \over {\log (4 ) - \log (5)}} \approx 68.1257\]

  18. anonymous
    • 5 years ago
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    there's a typo in the second line - it's supposed to be: (x+4) log 4 = (x-6) log 5 sry, about that...

  19. anonymous
    • 5 years ago
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    if you'll give me medal then here's the solution: 4^(x+4)=5^(x-6) => (x+4)log 4 = (x-6)log 5 =>(x+4)/(x-6) = log5/log 4 => (x+4)/(x-6) = 1.16 => (x+4) = 1.16 (x-6) =>1.16x -x = 4+1.16 (6) => x = 10.96/0.16 => x = 68.5

  20. anonymous
    • 5 years ago
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    if you solve this one I will give you a medal

  21. anonymous
    • 5 years ago
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    use log b 2=0.693 and /or log b7=1.946 to find log b 14 log b 14 = approximate the b is below log

  22. anonymous
    • 5 years ago
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    \[\log_{b} (2) = 0.693\] \[\log_{b} (7) = 1.946\] like this?

  23. anonymous
    • 5 years ago
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    yes

  24. anonymous
    • 5 years ago
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    okay - you just need to remember one simple fact: \[\log_{b}(x) = {\log_{k}(x) \over \log_{k}(b) }

  25. anonymous
    • 5 years ago
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    I have got this one wrong 5 times also

  26. anonymous
    • 5 years ago
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    \[\log_{b}(x) = {\log_{k}(x) \over \log_{k}(b) } \]

  27. anonymous
    • 5 years ago
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    okay what do I plug in where

  28. anonymous
    • 5 years ago
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    I got 2.808

  29. anonymous
    • 5 years ago
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    b is your unknown base and k is just some random base you can choose... for example \[\log_{15} (80) = { \log_{10}(80) \over \log_{10}(15) }\] so you got the base-10 logarithm on your calculator and can therefore calculate teh base-15 logarithm of 80...

  30. anonymous
    • 5 years ago
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    I just don't get it can you help me this please solve I just want to get this BS done it is my last problem

  31. anonymous
    • 5 years ago
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    I have tried so many different ways to solve it and emailed my professor and he is no help

  32. anonymous
    • 5 years ago
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    lol, one should do his/her assignment himself. just kidding, don't mind!!

  33. anonymous
    • 5 years ago
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    okay, okay - BUT, you rly should try to understand it, cause it's quite important. \[\log_{b}(2) = {\ln (2) \over \ln(b)} = 0.693\] \[\ln(b) = {\ln(2) \over 0.693}\] \[b = e ^ {\ln(2) \over 0.693} \approx e ^ 1 \approx 2.7183\] the last line is due to the fact, that ln(2) is about 0.6931... now you should try the same with the other fact you got and check the result.

  34. anonymous
    • 5 years ago
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    okay thank you

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