Задание 2.13

1) $2^x+2^{x-1}+2^{x-2}=3^x-3^{x-1}+3^{x-2}$
$2^{x-2}\left(2^{x-x+2}+2^{x-1-x+2}+1\right)=3^{x-1}\left(3^{x-x+2}-3^{x-1-x+2}+1\right)$
$2^{x-2}\left(4+2+1\right)=3^{x-2}(9-3+1)$
$7\cdot 2^{x-2}=7\cdot 3^{x-2}$
$2^{x-2}=3^{x-2}$(:$3^{x-2}$)
$\frac{2^{x-2}}{3^{x-2}}=1$
${\left(\frac{2}{3}\right)}^{x-2}=\left(\frac{2}{3}\right)$
$x-2=0$
$x=2$,
$:<!--\; FUNCTION\; APPLICATION\; -->2$.
2) $3^{x^2+2}-5^{x^2-1}=5^{x^2+1}+3^{x^2-1}$
$3^{x^2+2}-3^{x^2-1}=5^{x^2-1}+5^{x^2+1};$
$3^{x^2-1}\left(3^{x^2+2-x^2+1}-1\right)=5^{x^2-1}\left(1+5^{x^2+1-x^2+1}\right)$
$3^{x^2-1}(27-1)=5^{x^2-1}(1+25)$
$26\cdot 3^{x^2-1}=26\cdot 5^{x^2-1}$
$3^{x^2-1}=5^{x^2-1}(:5^{x^2-1})$
${\left(\frac{3}{5}\right)}^{x^2-1}=1$
${\left(\frac{3}{5}\right)}^{x^2-1}={\left(\frac{3}{5}\right)}^0$
$x^2-1=0$
$x^2=1$
$x=\pm 1$
Ответ:$x=\pm 1$
3) $7^x-5^{x+2}=2\cdot 7^{x-1}-118\cdot 5^{-x-1}$
$7^x-2\cdot 7^{x-1}=5^{x+2}-118\cdot 5^{x-1}$
$7^{x-1}(7-2)=5^{x-1}\left(5^3-118\right)$
$7^{x-1}5=5^{x-1}(125-118)$
$7^{x-1}\cdot 5=5^{x-1}\cdot 7$
$\frac{7^{x-1}}{5^{x-1}}=\frac{7}{5}$
${\left(\frac{7}{5}\right)}^{x-1}={\left(\frac{7}{5}\right)}^1$
$x-1=1$
$x=2.$
Ответ: $x=2.$