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 June 8th, 2016, 10:18 AM #1 Newbie   Joined: Jun 2016 From: U.Sa Posts: 1 Thanks: 0 Help with a few log equations A few problems that I'm a little stumped on. A) e^x + 6e^-x - 7 =0 What I tried to do here is move the 6e^-x to the right and convert to natural log. So. ln(e^x-7)=ln (-6e^-x) or ln -6 + -x on the right. Since ln e to an exponent is the exponent. After that I'm stumped. I assume I can make the left side x ln (e-7) = ln -6 + -x but I'm lost after that. B) log base 3 (x-2) + log base 3 (2x-3) = 5 log base 3 (x) I subtracted the right and made it into log base 3 (x-2)(2x-3)/x^5 but that's it. June 8th, 2016, 10:39 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,656 Thanks: 2634 Math Focus: Mainly analysis and algebra A) Multiply the original equation through by $\mathrm e^{x}$ and note that $\mathrm e^{2x}=(\mathrm e^x)^2$ B) From where you are use $3^{\log_3 y} = y$ Last edited by v8archie; June 8th, 2016 at 10:41 AM. June 10th, 2016, 06:00 AM   #3
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Quote:
 Originally Posted by Sudowoodo A few problems that I'm a little stumped on. A) e^x + 6e^-x - 7 =0
Multiply through by e^x to get e^(2x)+ 6- 7e^x= (e^x)^2- 7e^x+ 6= 0. Now let y=e^x. Can you solve y^2- 7y+ 6= 0?

Quote:
 What I tried to do here is move the 6e^-x to the right and convert to natural log. So. ln(e^x-7)=ln (-6e^-x) or ln -6 + -x on the right. Since ln e to an exponent is the exponent. After that I'm stumped. I assume I can make the left side x ln (e-7) = ln -6 + -x but I'm lost after that. B) log base 3 (x-2) + log base 3 (2x-3) = 5 log base 3 (x) I subtracted the right and made it into log base 3 (x-2)(2x-3)/x^5 but that's it.
I hope you mean you changed it to log_3((x-2)(2x-3)/x^5)= 0. So what number has log, base 3, equal to 0? (What is 3^0?) Tags equations, log Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Ismael Calculus 2 August 23rd, 2014 05:27 PM Ismael Calculus 0 August 23rd, 2014 03:56 PM ZeusTheMunja Linear Algebra 20 January 25th, 2013 05:52 AM maximade Calculus 4 June 15th, 2010 07:37 PM cafegurl Algebra 6 August 3rd, 2009 07:58 AM

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