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anonymous

  • one year ago

Express as a single logarithm. log6496 – log62 I know logs pretty well but I don't know how to express 2 logs as a single log, can someone please help??

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  1. anonymous
    • one year ago
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    I meant log base 6 of 496 - log base 6 of 2

  2. anonymous
    • one year ago
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    \[\log_{6} 496-\log_{6} 2=\log_{6} \frac{ 496 }{ 2 }=\log_{6} 248\]

  3. anonymous
    • one year ago
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    That's what I thought thank you! What about, log base 5 of 50 + log base 5 of 2.5?

  4. anonymous
    • one year ago
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    I know it has to equal something in the final answer and that confuses me

  5. Nnesha
    • one year ago
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    quotient rule\[\large\rm log_b x - \log_b y = \log_b \frac{ x }{ y}\] to condense you can change subtraction to division product rule \[\large\rm log_b x + \log_b y = \log_b( x \times y )\] addition ----> multiplication power rule \[\large\rm log_b x^y = y \log_b x\] you should familiar with these

  6. Nnesha
    • one year ago
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    there is a plus sign so which property you should apply ?

  7. anonymous
    • one year ago
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    the product property

  8. Nnesha
    • one year ago
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    yes right

  9. anonymous
    • one year ago
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    I am doing a test review and all of the multiple choice answers for the question equal something, like one answer is, log base 5 of 125=3

  10. anonymous
    • one year ago
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    How do you find what it equals?

  11. Nnesha
    • one year ago
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    log base 5 of 50 + log base 5 of 2.5 for this question ?

  12. anonymous
    • one year ago
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    yes

  13. Nnesha
    • one year ago
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    \[\huge\rm log_5 50+ \log_5 2.5\] is this ur question ?

  14. anonymous
    • one year ago
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    yes

  15. Nnesha
    • one year ago
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    there isn't an equal sign..

  16. anonymous
    • one year ago
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    These are the possible answers: \[\log_{5}125=3 \] \[\log_{5}112.5=2.93 \] \[\log_{5}112.5=22.5 \] \[\log_{5}125=625 \]

  17. Nnesha
    • one year ago
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    alright then you have to apply the `change of base` formula \[\huge\rm log_b a= \frac{ \log a }{ \log b }\]

  18. Nnesha
    • one year ago
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    \[\huge\rm log_5 50+ \log_5 2.5\] first) how would you write this in single log form b applying product property ?

  19. anonymous
    • one year ago
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    \[\log_{5}125 \] ?

  20. Nnesha
    • one year ago
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    yes right now use change of base formula

  21. anonymous
    • one year ago
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    How do I know what to change the base to?

  22. Nnesha
    • one year ago
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    base would stay the same hmm what do you mean ? o.O here is an example \[\log_2 3 =\frac{ \log(3) }{ \log(2) }\]

  23. anonymous
    • one year ago
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    oh okay! I was looking at my notes and I read the equation wrong!

  24. Nnesha
    • one year ago
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    ohh

  25. anonymous
    • one year ago
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    soooo is the answer \[\log_{5}125=3 \]

  26. Nnesha
    • one year ago
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    if log_5 (125) is equal to 3 then yes did you use the formula ?

  27. Nnesha
    • one year ago
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    how would you use `change of base formula` for \[\large\rm \log_5 125\]

  28. anonymous
    • one year ago
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    \[\frac{ \log(125) }{ \log(5) }\]

  29. Nnesha
    • one year ago
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    perfect!

  30. anonymous
    • one year ago
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    Awesome! This makes sense now! Thank you so much! You are very smart

  31. Nnesha
    • one year ago
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    glad to hear that & thanks & good job! good luck !

  32. anonymous
    • one year ago
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    Thanks! :)

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