Помогите решить, пожалуйста. Created by Esnc. matematika-ru

Помогите решить, пожалуйста...

Esnc @Esnc

November 2021 1 14 Report

Помогите решить, пожалуйста

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sedinalana

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1
(1/4)^(10x)<(1/4)^(x²-8/3)
Основание меньше 1,знак меняется
10x>x²-8/3
x²-10x-8/3<0
3x²-30x-8<0
D=900+96=996
x1=(30-2√249)/6=(15-√249)/3 U x=(15+√249)/3
x∈((15-√249)/3;(15+√249)/3)
2
3*(1/3)^2x-10*(1/3)^x+3<0
(1/3)^x=a
3a²-10a+3<0
D=100-36=64
a1=(10-8)/6=1/3 U a2=(10+8)/6=3
1/3<a<3⇒1/3<(1/3)^x<3⇒-1<x<1
x∈(-1;1)
3
8^2x-8*8^x-8>0
8^x=a
a²-8a-8>0
D=64+32=96
a1=(8-4√6)/2=4-2√6 U a2=4+2√6
a<4-2√6⇒8^x<4-2√6 нет решения
a>4+2√6⇒8^x>4+2√6⇒x>log(8)(4+2√6)
x∈(log(8)(4+2√6);∞)

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