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 June 26th, 2018, 02:24 PM #1 Newbie   Joined: Apr 2018 From: Banovo Brdo Posts: 12 Thanks: 0 Logarithms $\left(\sqrt{\log_7\left(-2x-1\right)}-\log_7\sqrt{4x^2+4x+1}-1\right)\cdot \log_7\left|x+7\right|=-3\log_7\sqrt[3]{x+7}$ What are the solutions to this equation? I got -6 and -4, but I think it should be -6 and -5? Thanks. EDIT: Never mind, solved. Last edited by greg1313; June 26th, 2018 at 06:51 PM.
 June 26th, 2018, 02:48 PM #2 Senior Member   Joined: Aug 2012 Posts: 2,157 Thanks: 631 Hi bongcloud. It's legal where I live. Thanks from Joppy
 June 26th, 2018, 03:54 PM #3 Global Moderator   Joined: Dec 2006 Posts: 20,285 Thanks: 1967 I'll assume that $x + 7 > 0$. If $7^{n^2} = -2x - 1$, where $n \geqslant 0$ and $-2x - 1 > 0$, $n - n^2 - 1 = -1$, and so $n$ is 1 or 0. Hence $-2x - 1$ = 7 or 1, and so $x$ = -4 or -1.

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