Results 1 to 3 of 3

Thread: Trying to understand exponents and logs

  1. #1
    Newbie
    Joined
    Jan 2017
    From
    Boise, Id
    Posts
    1

    Trying to understand exponents and logs

    Let me try this again, without word formatting.


    Somewhat new to algebra 54-year-old took up math as a hobby<br>I am not sure if this is a log question or exponent question but in the equation
    log 3.0112 = 1050
    mathematically how do you get 1050 from 3.0211. I mean I understand log10 = 1, log100 = 2, log3 = 1000, etc. But the decimal points in-between are a mystery. I get stuck after 10*10*10= 3.0, where does the .0211 come in to get 1050<br>
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,047
    Thanks
    3621

    Re: Trying to understand exponents and logs

    In future, do not make a new post covering the same problem ... attach your correction to your initial post. Thank you.

    log 3.0112 = 1050
    $\log_b(y) = x \implies b^x = y$

    ... maybe you meant to type $\log(1050) = 3.0212$ ?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,185
    Thanks
    2818

    Re: Trying to understand exponents and logs

    Quote Originally Posted by johnymac67 View Post
    Let me try this again, without word formatting.


    Somewhat new to algebra 54-year-old took up math as a hobby<br>I am not sure if this is a log question or exponent question but in the equation
    log 3.0112 = 1050
    mathematically how do you get 1050 from 3.0211. I mean I understand log10 = 1, log100 = 2, log3 = 1000, etc. But the decimal points in-between are a mystery. I get stuck after 10*10*10= 3.0, where does the .0211 come in to get 1050<br>
    Are we to assume that this logarithm is to base 10? "log(3.0112)= 1050" is false. No is it true that log(1050)= 3.0112! What is true is that log(1050)= 3.0211. That is true because 10^{3.0211}= 1050 (to the nearest integer). You know that 10^3= 1000. You also, I presume, know that 10^{3.0211 10^{3+ 0.0211}= (10^3)(10^{0.0211}). The rest is true because 10^{0.0211}= 1.050.

    How do we determine that? There are a number of (very tedious) numerical ways of calculating that.

    Fortunately other people have already done that and put the values into tables that were put into books. And today, we have calculators that find logarithms and exponentials. Enter 1050 into the calculator that comes with Windows, click on the 'log' "key" and you get 3.0211892990699380727935052671233 which rounds to 3.0211 (not 3.0112).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Exponents and Logs
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Jun 2nd 2010, 06:36 PM
  2. Exponents as logs?
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Nov 13th 2009, 10:45 AM
  3. Logs and Exponents
    Posted in the Algebra Forum
    Replies: 3
    Last Post: Jan 18th 2009, 03:35 PM
  4. exponents and logs
    Posted in the Algebra Forum
    Replies: 7
    Last Post: May 15th 2007, 01:52 PM

/mathhelpforum @mathhelpforum