Solve: ln(x – 3) = ln(7x – 23) – ln(x + 1)

1 answer:

8 0

$Formula\ for\ lagarythm:\\
log_ab=c\ \ \ ----> a^c=b\\\\Base\ of\ ln \ is\ e=2,7\\\\ln(x-3)=ln(7x-23)-ln(x+1)\\\\
ln(x-3)=ln(\frac{7x-23}{x+1})\ \ \ | subtract\ ln(\frac{7x-23}{x+1})\\\\
ln(\frac{\frac{7x-23}{x+1}}{x-3})=0\\\\
ln(\frac{7x-23}{(x+1)(x-3)})=0\\\\
2,7^0=\frac{7x-23}{(x+1)(x-3)}\\\\
1=\frac{7x-23}{(x+1)(x-3)}\ \ \ | multiply\ by\ (x+1)(x-3)\\\\
(x+1)(x-3)=7x-23\\\\
x^2-3x+x-3=7x-23\\\\
x^2-9x-26=0\\\\x=\frac{1}{2}(9-\sqrt{185})\ \ or\ \ x=\frac{1}{2}(9+\sqrt{185})
$

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images attached showing all working

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