Question

Решите уравнение: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Answer 1

1.
$6^{x}=216 , \\ 6^{x}=6^3 , \\ x=3.$
2.
$2^{3x-5}=16, \\ 2^{3x-5}=2^4, \\ 3x-5=4, \\ 3x=9, \\ x=3.$
3.
$3^{ x^{2} -5x+2} = \frac{1}{81} , \\ 3^{ x^{2} -5x+2} = 3^{-4}, \\ x^{2} -5x+2=-4, \\ x^{2} -5x+6=0, \\ x_1=2, x_2=3.$
4.
$3\cdot( \frac{2}{5}) ^{x}= \frac{12}{25} , \\ ( \frac{2}{5}) ^{x}= \frac{4}{25} , \\ ( \frac{2}{5}) ^{x}= (\frac{2}{5})^2 , \\ x=2.$
5.
$5^{x-1}+ 5^{x}=150 , \\ \frac{5^{x}}{5}+ 5^{x}=150 , \\ 5^{x}(\frac{1}{5}+1)=150 , \\ 5^{x}\cdot\frac{6}{5}=150 , \\ 5^{x}=125 , \\ 5^{x}=5^3 , \\ x=3.$
6.
$(0,7)^{x}=0,343, \\ (0,7)^{x}=(0,7)^3, \\ x=3.$
7.
$4^{3-x}= \frac{1}{64}, \\ 4^{3-x}=4^{-3}, \\ 3-x=-3, \\ x=6.$
8.
$( \frac{1}{5}) ^{ x^{2} +x-10}=625, \\ ( \frac{1}{5}) ^{ x^{2} +x-10}=( \frac{1}{5}) ^{-4}, \\ x^{2} +x-10=-4, \\ x^{2} +x-6=0, \\ x_1=-3, x_2=2.$
9.
$( \frac{4}{3}) ^{ x^{2} -1,5} = \sqrt{0,75} , \\ ( \frac{4}{3}) ^{ x^{2} -1,5} = ( \frac{4}{3}) ^{ - \frac{1}{2} } , \\ x^{2} -1,5=-0,5, \\ x^{2} -1=0, \\ (x+1)(x-1)=0, \\ x_1=-1;x_2=1.$
10.
$2^{2 x -3}+ 2^{2x+1}=136, \\ 2^{2x}(2^{-3}+ 2)=136, \\ 2^{2x}(\frac{1}{8}+ 2)=136, \\ 2^{2x}\cdot\frac{17}{8}=136, \\ 2^{2x}=64, \\ 2^{2x}=2^6, \\ 2x=6, \\ x=3.$