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June 2022 1 9 Report

Решите уравнение:
1. [tex](0,4) ^{x} =0,0256 [/tex]
2. [tex] 5^{4-3x}=125 [/tex]
3. [tex] 7^{ x^{2} -x-5}= \frac{1}{343} [/tex]
4. [tex](0,6) ^{ x^{2} } = \sqrt[3]{( 1\frac{2}{3}) ^{x} } [/tex]
5. [tex] 3^{3x-1}- 3^{3x+2}=-234 [/tex]

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arsenlevadniy

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1.
$(0,4) ^{x} =0,0256 , \\ (0,4) ^{x} =(0,4) ^{4} , \\ x=4.$
2.
$5^{4-3x}=125 , \\ 5^{4-3x}=5^3 , \\ 4-3x=3, \\ -3x=-1, \\ x= \frac{1}{3} .$
3.
$7^{ x^{2} -x-5}= \frac{1}{343} , \\ 7^{ x^{2} -x-5}= 7^{-3} , \\ x^{2} -x-5=-3, \\ x^{2} -x-2=0, \\ x_1=-1, x_2=2.$
4.
$(0,6) ^{ x^{2} } = \sqrt[3]{( 1\frac{2}{3}) ^{x} } , \\ ( \frac{3}{5} ) ^{ x^{2} } = \sqrt[3]{( \frac{5}{3}) ^{x} } , \\ ( \frac{3}{5} ) ^{ x^{2} } = ( \frac{5}{3}) ^{- \frac{x}{3} } , \\ x^2=- \frac{x}{3} ,\\ x^2+\frac{x}{3}=0,\\ x(x+\frac{1}{3})=0,\\ x_1=- \frac{1}{3} , x_2=0.$
5.
$3^{3x-1}- 3^{3x+2}=-234 , \\ 3^{3x}(3^{-1}- 3^{2})=-234 , \\ 3^{3x}( \frac{1}{3} - 9)=-234 , \\ 3^{3x}(- \frac{26}{3} )=-234 , \\ 3^{3x}=27 , \\ 3^{3x}=3^3 , \\ 3x=3, \\ x=1.$

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