Question

$(\frac{5}{6} )^{x-1} *(\frac{4}{5} )^{x} = \frac{16}{45}$
Решите уравнение с объяснением шагов.

Answer 1

Ответ:

3

Объяснение:

(5/6)^x*(4/5)^x=(16/45)*(5/6)

(2/3)^x=8/27

(2/3)^x=(2/3)^3

x=3

Answer 2

$\displaystyle\bf\\\Big(\frac{5}{6} \Big)^{x-1} \cdot\Big(\frac{4}{5} \Big)^{x}=\frac{16}{45} \\\\\\\Big(\frac{5}{6} \Big)^{x} \cdot\Big(\frac{5}{6} \Big)^{-1} \cdot\Big(\frac{4}{5} \Big)^{x}=\frac{16}{45} \\\\\\\Big(\frac{5}{6} \cdot\frac{4}{5} \Big)^{x} \cdot\Big(\frac{6}{5} \Big)=\frac{16}{45} \\\\\\\Big(\frac{4}{6} \Big)^{x} \cdot\Big(\frac{6}{5} \Big)=\frac{16}{45} \\\\\\\Big(\frac{2}{3} \Big)^{x} =\frac{16}{45} :\frac{6}{5}$

$\displaystyle\bf\\\Big(\frac{2}{3} \Big)^{x} =\frac{16}{45}\cdot \frac{5}{6} \\\\\\\Big(\frac{2}{3} \Big)^{x} =\frac{8}{27}\\\\\\\Big(\frac{2}{3} \Big)^{x} =\Big(\frac{2}{3} \Big)^{3} \\\\\\\boxed{x=3}$