Question

Rezolvati ecuatiile logaritmice:

$log_{3x+5} (9 x^{2} +8x+3) = 2$
$log_{2} (x+2) - log_{2} (x-5) = 3$

Answer 1

$log_{3x+5}(9x^2 +8x+3)=2$
$9x^2+8x+3=(3x+5)^2$
$9x^2+8x+3=9x^2+25+30x$
22x=-22 => x = -1 


$log_2(x+2)-log_2(x-5)=3$
$log_2 \frac{x+2}{x-5} = 3$
$\frac{x+2}{x-5} = 8$
x+2=8(x-5)
x = 6