Algebra Pre-Algebra and Basic Algebra Math Forum

 April 22nd, 2014, 07:20 PM #1 Newbie   Joined: Apr 2014 From: South Florida Posts: 8 Thanks: 1 Exponential Quadratic This problem popped up on my homework: $\displaystyle 7^{2x+1}-15•7^x+2=0$ Is the $\displaystyle 2x+1$ just a typo? Can this be done? Note that my teacher is very prone to making typos. I did the problem assuming that it was just $\displaystyle 7^{2x}$ and got $\displaystyle x=log_7\left({15\pm\sqrt{218}\over 2}\right)$. Thanks. April 22nd, 2014, 07:30 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,700 Thanks: 2682 Math Focus: Mainly analysis and algebra \begin{align*} 7^{2x+1}-15 \cdot 7^x+2 &= 0 \\ 7 \cdot 7^{2x}-15 \cdot 7^x+2 &= 0 \\ \left( 7 \cdot 7^x - 1\right) \left( 7^x - 2 \right) &= 0 \\ \left( 7^{x+1} - 1\right) \left( 7^x - 2 \right) &= 0 \\ \end{align*} So $$\left(x + 1\right)\log{7} = 0 \; \Longrightarrow \; x = -1$$ or $$x\log{7} = \log{2} \; \Longrightarrow \; x = \frac{\log{2}}{\log{7}}$$ I like my numbers better than yours. Thanks from scomora Last edited by v8archie; April 22nd, 2014 at 07:36 PM. April 22nd, 2014, 07:53 PM   #3
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 Originally Posted by v8archie \begin{align*} 7^{2x+1}-15 \cdot 7^x+2 &= 0 \\ 7 \cdot 7^{2x}-15 \cdot 7^x+2 &= 0 \\ \left( 7 \cdot 7^x - 1\right) \left( 7^x - 2 \right) &= 0 \\ \left( 7^{x+1} - 1\right) \left( 7^x - 2 \right) &= 0 \\ \end{align*} So $$\left(x + 1\right)\log{7} = 0 \; \Longrightarrow \; x = -1$$ or $$x\log{7} = \log{2} \; \Longrightarrow \; x = \frac{\log{2}}{\log{7}}$$ I like my numbers better than yours. I like yours a lot more too! Never thought of it like that. Thanks a lot  April 22nd, 2014, 09:38 PM #4 Global Moderator   Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms An alternate approach: let y = 7^x and replace 7^(2x+1) with 7y^2. Tags exponential, quadratic 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 katiekapp Algebra 5 January 25th, 2012 06:47 PM Alvy Calculus 2 May 24th, 2010 09:30 AM winterbegins Calculus 6 August 12th, 2009 10:10 PM katiekapp Calculus 1 December 31st, 1969 04:00 PM Orimagi Calculus 1 December 31st, 1969 04:00 PM

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