My Math Forum Logarithm help please!

 Pre-Calculus Pre-Calculus Math Forum

December 3rd, 2018, 07:18 PM   #1
Newbie

Joined: Dec 2018
From: New Zealand

Posts: 1
Thanks: 1

No clue on where to start.
Attached Images
 20181204_171725.jpg (98.7 KB, 9 views)

 December 3rd, 2018, 08:22 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,458 Thanks: 1340 all logs are base 10 $\log(x+5) = 2 - \log(x)$ $\log(x+5)+\log(x) = 2$ $\log((x+5)(x)) = 2$ $\log(x^2+5x)=2$ $x^2 + 5x = 100$ $x^2 + 5x - 100 = 0$ $x = \dfrac{-5\pm \sqrt{425}}{2}$ $x = \dfrac 5 2 \left(-1 \pm \sqrt{17}\right)$ but..... we have to check these in the original equation. $\dfrac 5 2 (-1 - \sqrt{17}) < 0$ and thus cannot be used as an argument to the $\log()$ function. so the final answer is $x = \dfrac 5 2 (-1 + \sqrt{17})$ Thanks from greg1313
 December 4th, 2018, 05:40 AM #3 Senior Member   Joined: May 2016 From: USA Posts: 1,310 Thanks: 551 With all the great deference that is due to romsek, the steps that he does not show are exactly the ones that I have found beginning students stumble over. Starting at this line $\log_{10}(x^2 + 5x) = 2 \implies$ $\log_{10}(x^2 + 5x) = 2 * 1 \implies$ $\log_{10}(x^2 + 5x) = 2 * \log_{10}(10) \implies$ $\log_{10}(x^2 + 5x) = \log_{10}(10^2) \implies$ $\log_{10}(x^2 + 5x) = \log_{10}(100) \implies$ $antilog\{\log(x^2 + 5x)\} = antilog\{\log(100)\} \implies$ $x^2 + 5x = 100.$ The step of equating a number with the logarithm of the base raised to the power of that number is something that seems automatic to those who are familiar with logarithms, but, at least among my students, simply does not come to mind initially. The step of equating arguments was more intuitive to those of us who were trained to use logs and antilogs for real-life calculation (back when mammoths and woolly rhinos roamed in Central Park). I have never had a student who had been given any theoretical justification for that step, which is ridiculous because students are taught about the inverses of functions. Thanks from greg1313 Last edited by skipjack; December 4th, 2018 at 02:22 PM.

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post stoik Algebra 2 March 18th, 2014 08:48 AM sachinrajsharma Algebra 4 February 18th, 2013 07:10 PM jsmith613 Algebra 12 November 29th, 2010 05:51 PM jsmith613 Algebra 4 November 28th, 2010 09:27 AM football Algebra 10 August 2nd, 2010 10:57 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top