Solve for x : 2+ (x+3)- (3 x-5)= 3 - Vidyadip

Question

Solve for $\mathrm{x}$ :$\log 2+\log (x+3)-\log (3 x-5)=\log 3$

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Answer

$ \log 2+\log (x+3)-\log (3 x-5)=\log 3$
$\therefore \log 2(x+3)-\log (3 x-5)=\log 3 \ldots . .[\because \log m+\log n=\log m n]$
$\therefore \log \frac{2(x+3)}{3 x-5}=\log 3 \ldots . .\left[\because \log m-\log n=\log \frac{m}{n}\right]$
$\therefore \frac{2(x+3)}{3 x-5}=3$
$\therefore 2 x+6=9 x-15$
$\therefore 7 x=21$
$\therefore x=3 $
Check:
If $x=3$ satisfies the given condition, then our answer is correct.
$ \text { L.H.S. }=\log 2+\log (x+3)-\log (3 x-5)$
$=\log 2+\log (3+3)-\log (9-5)$
$=\log 2+\log 6-\log 4$
$=\log (2 \times 6)-\log 4$
$=\log \frac{12}{4}$
$=\log 3$
$=\text { R.H.S. } $
Thus, our answer is correct.

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