Question

Помогите с примерами по теме "Показательные уравнения"

Answer 1

a)

$(\frac{1}{7}^x^-^2=7^3^n^-^2\\\\7^-^x^+^2=7^3^x^-^2\\\\-x+2=3x-2\\\\-x-3x=-2-2\\\\-4x=-4\\\\x=1$

б)

$(\frac{1}{\sqrt{5} })^2^x^-^1=(25\sqrt{5})^x^-^1\\\\5^-^\frac{1}{2}^*^(^2^x^-^1^)=5^\frac{5}{2}^*^(^x^-^1^)\\\\5^-^x^+^\frac{1}{2}=5^\frac{5}{2}^x^-^\frac{5}{2}\\\\-x+\frac{1}{2}=\frac{5}{2}x-\frac{5}{2}\\\\-2x+1=5x-5\\\\-2x-5x=-5-1\\\\-7x=-6\\\\x=\frac{6}{7}$

в)

$\frac{0,1*0,001^x}{\sqrt{10} }=10000*\sqrt{10}\\\\\frac{10^-^1*10^-^2^x}{10^\frac{1}{2} }=10^\frac{9}{2}\\\\\frac{10^-^2^x^-^1}{10^\frac{1}{2} }=10^\frac{9}{2}\\\\10^-^2^x^-^\frac{3}{2}=10^\frac{9}{2}\\\\-2x-\frac{3}{2}=\frac{9}{2}\\\\-2x=\frac{9}{2}+\frac{3}{2}\\\\-2x=6\\\\x=-3$