Question

Determinati x € R ,știind ca :
a) 2x supra5 = 125 supra 8x
b) 4x supra 27 =3 supra x
c) 3x supra 16 =1 supra 27 x
d)36 supra 3x =75x supra 9
e) 9 supra 5x=20x supra 4
f)4 supra 6x=54 x supra 25
URGEEENT!!Dau coroană!!!

Answer 1

$a) \frac{2x}{5} = \frac{125}{8x}$

$8x \times 2x = 125 \times 5$

$16 {x}^{2} =625$

${x}^{2} = \frac{625}{16}$

$x = \pm \sqrt{ \frac{625}{16} }$

$x = \pm \frac{ \sqrt{625} }{ \sqrt{16} }$

$x = \pm \frac{25}{4}$

$b) \frac{4x}{27} = \frac{3}{x}$

$4x \times x = 3 \ \times 27$

$4 {x}^{2} = 81$

${x}^{2} = \frac{81}{4}$

$x = \pm \sqrt{ \frac{81}{4} }$

$x = \pm \frac{ \sqrt{81} }{ \sqrt{4} }$

$x = \pm \frac{9}{2}$

$c) \frac{3x}{16} = \frac{1}{27x}$

$3x \times 27x = 1 \times 16$

$81 {x}^{2} = 16$

${x}^{2} = \frac{16}{81}$

$x = \pm \sqrt{ \frac{16}{81} }$

$x = \pm \frac{ \sqrt{16} }{ \sqrt{81} }$

$x = \pm \frac{4}{9}$

$d) \frac{36}{3x} = \frac{75x}{9}$

$3x \times 75x = 36 \times 9$

$225 {x}^{2} = 324$

${x}^{2} = \frac{324}{225}$

$x = \pm \sqrt{ \frac{324}{225} }$

$x = \pm \frac{ \sqrt{324} }{ \sqrt{225} }$

$x = \pm \frac{18}{15}$

$x = \pm \frac{6}{5}$

$e) \frac{9}{5x} = \frac{20x}{4}$

$5x \times 20x = 9 \times 4$

$100 {x}^{2} = 36$

${x}^{2} = \frac{36}{100}$

$x = \pm \sqrt{ \frac{36}{100} }$

$x = \pm \frac{ \sqrt{36} }{ \sqrt{100} }$

$x = \pm \frac{6}{10}$

$x = \pm \frac{3}{5}$

$f) \frac{4}{6x} = \frac{54x}{25}$

$6x \times 54x = 4 \times 25$

$324 {x}^{2} = 100$

${x}^{2} = \frac{100}{324}$

$x = \pm \sqrt{ \frac{100}{324} }$

$x = \pm \frac{ \sqrt{100} }{ \sqrt{324} }$

$x = \pm \frac{10}{18}$

$x = \pm \frac{5}{9}$