Results 1 to 4 of 4

Math Help - a basic logarithmic inquiry...

  1. #1
    Newbie
    Joined
    Feb 2013
    From
    New York
    Posts
    3

    a basic logarithmic inquiry...

    hello--

    It is understood that a logarithmic notation:



    That is certainly straight forward. But, please clarify: how to correlate the above expression with the following:


    10 log 2 = 3

    10 log 10 = 10

    10 log 1,000,000 = 60

    Even entering a calculator elicits the above, but I am unable to relate "10 log 1000000 = 60" to (merely as an example) "log 2 (8) = 3"

    I can do the math for "log 2 (8) = 3" (I am multiplying 2 by itself 3 times to produce 8) but I cannot explain how (again, only as an example) "
    10 log 1,000,000 = 60"


    I hesitate to pose this inquiry only because I feel certain the explanation will appear quite obvious...

    thank you!





    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member jakncoke's Avatar
    Joined
    May 2010
    Posts
    387
    Thanks
    80

    Re: a basic logarithmic inquiry...

    Calculators usually do base 10 logs.

    log rules say  a log_b (x) = log_b(x^a)

    so 10 log 10 or  10 log_{10} (10) = log_{10}(10^{10}) = 10
    same applies for all the other expression you provided.

    basically ask your self, base b raised to what power gives the expression inside the log.

     log_2{8} = log_2{2^3} (2 raised to what power gives me 2^3 ? 3, so  log_2{2^3} = 3
    Last edited by jakncoke; February 21st 2013 at 12:46 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123

    Re: a basic logarithmic inquiry...

    Quote Originally Posted by stonewhite View Post
    hello--

    It is understood that a logarithmic notation:



    That is certainly straight forward. But, please clarify: how to correlate the above expression with the following:


    10 log 2 = 3

    10 log 10 = 10

    10 log 1,000,000 = 60

    Even entering a calculator elicits the above, but I am unable to relate "10 log 1000000 = 60" to (merely as an example) "log 2 (8) = 3"

    I can do the math for "log 2 (8) = 3" (I am multiplying 2 by itself 3 times to produce 8) but I cannot explain how (again, only as an example) "
    10 log 1,000,000 = 60"


    I hesitate to pose this inquiry only because I feel certain the explanation will appear quite obvious...

    thank you!
    All the logarithms you mentioned above use (nearly!) the base 10.

    10 \cdot \log_{10}(10)=10~\implies~\log_{10}(10)=1~\implies  ~10^1=10

    and

    10 \cdot \log_{10}(1,000,000)=60 \implies \log_{10}(1,000,000)=6 \implies \\ \\ 10^6=1,000,000

    Only

    10 \cdot \log_{10}(2)=3~\implies~\log_{10}(2)=0.3~\implies~  10^{0.3}\approx 2

    is a very roughly rounded value.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Feb 2013
    From
    New York
    Posts
    3

    Re: a basic logarithmic inquiry...

    thank you both!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [Complex Numbers] Inquiry about relationship
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: April 22nd 2012, 05:27 AM
  2. Inquiry about proofs involving families of sets
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: January 11th 2012, 07:14 AM
  3. Law of logarithm inquiry
    Posted in the Algebra Forum
    Replies: 4
    Last Post: January 21st 2011, 06:20 AM
  4. Replies: 1
    Last Post: April 5th 2009, 04:11 PM
  5. Replies: 2
    Last Post: October 2nd 2008, 04:08 AM

Search Tags


/mathhelpforum @mathhelpforum