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Question Number 190961 by pascal889 last updated on 15/Apr/23

	Answered by cortano12 last updated on 16/Apr/23
	$⇒log _(10) (3x^2 +8)=log _(10) (5x+10) ⇒3x^2 −5x−2=0 ⇒(3x+1)(x−2)=0 ⇒ { ((x=−(1/3))),((x=2)) :}$
	$\Rightarrow \log_{10} ({3 x}^{2} + 8) = \log_{10} (5 x + 10)$ $\Rightarrow {3 x}^{2} - 5 x - 2 = 0$ $\Rightarrow (3 x + 1) (x - 2) = 0$ $\Rightarrow {\begin{cases} x = - \frac{1}{3} \\ x = 2 \end{cases}$
	Commented by pascal889 last updated on 15/Apr/23

	$p l e a s e i d o n t r e a l l y g e t u r w o r k i n g s$
	Answered by manxsol last updated on 15/Apr/23

	$l o g (3 x^{2} + 8) = l o g 10 + l o g (\frac{x}{2} + 1)$ $x > - 2$ $l o g (3 x^{2} + 8) = l o g (5 x + 10)$ $3 x^{2} + 8 = 5 x + 10$ $3 x^{2} - 5 x - 2 = 0$ $(3 x + 1) (x - 2) = 0$ $x = - \frac{1}{3}$ $x = 2$
	Answered by Rasheed.Sindhi last updated on 15/Apr/23

	$\log_{10} (3 x^{2} + 8) - \log_{10} (\frac{x + 2}{2}) = \log_{10} 10$ $\log_{10} \frac{3 x^{2} + 8}{\frac{x + 2}{2}} = \log_{10} 10$ $\frac{3 x^{2} + 8}{\frac{x + 2}{2}} = 10$ $3 x^{2} + 8 = 10 (\frac{x + 2}{2}) = 5 x + 10$ $3 x^{2} - 5 x - 2 = 0$ $(x - 2) (3 x + 1) = 0$ $x = 2 o r x = - \frac{1}{3}$
	Commented by pascal889 last updated on 15/Apr/23

	$t h a n k s s i r$
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