Logarithms

Apr 2018
12
0
Banovo Brdo
$\left(\sqrt{\log_7\left(-2x-1\right)}-\log_7\sqrt{4x^2+4x+1}-1\right)\cdot \log_7\left|x+7\right|=-3\log_7\sqrt[3]{x+7}$

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 a moderator:

skipjack

Forum Staff
Dec 2006
21,481
2,470
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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