Решите уравнение:1. [latex] 6^{x}=216 [/latex]2. [latex] 2^{3x-5}=16 [/latex]3. [latex] 3^{ x^{2} -5x+2} = \frac{1}{81} [/latex]4. [latex]3*( \frac{2}{5}) ^{x}= \frac{12}{25} [/latex]5. [latex] 5^{x-1}+ 5^{x}=150 [/latex]6. [l...

1. [latex] 6^{x}=216 , \\ 6^{x}=6^3 , \\ x=3. [/latex] 2. [latex] 2^{3x-5}=16, \\ 2^{3x-5}=2^4, \\ 3x-5=4, \\ 3x=9, \\ x=3.[/latex] 3. [latex] 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.[/latex] 4. [latex]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.[/latex] 5. [latex] 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.[/latex] 6. [latex](0,7)^{x}=0,343, \\ (0,7)^{x}=(0,7)^3, \\ x=3.[/latex] 7. [latex] 4^{3-x}= \frac{1}{64}, \\ 4^{3-x}=4^{-3}, \\ 3-x=-3, \\ x=6.[/latex] 8. [latex]( \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.[/latex] 9. [latex]( \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.[/latex] 10. [latex] 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.[/latex]