log₁₄₄(3-x)²=log₁₂√3x-5 log₅x+logₓ25=3. Created by ggggraanat. algebra-ru

log₁₄₄(3-x)²=log₁₂√3x-5 log₅x+logₓ25=3...

July 2022 1 15 Report

log₁₄₄(3-x)²=log₁₂√3x-5
log₅x+logₓ25=3

Answers & Comments

MizoriesKun ㏒₁₄₄ (3-х)²= ㏒₁₂√(3х-5) (144=12²)

2*(1/2)㏒₁₂ (3-х)= ㏒₁₂√(3х-5)

㏒₁₂ (3-х)= ㏒₁₂√(3х-5) ОДЗ 3-х>0 x<3 ; 3х-5>0 x> 5/3

(3-х)= √(3х-5) возведем обе части в квадрат

(3-х)²= √(3х-5) ²

9-6х+х²=3х-5

х²-9х+14=0

D=81-56=25 √D=5

x₁=(9+5)/2=7 не подходит под ОДЗ

x₂=(9-5)/2=2

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log₅x+logₓ25=3

log₅x+ 1/log₂₅х=3

log₅x+ 2/log₅х=3 замена log₅x = а

а+ 2/а=3

а²-3а+2=0

D=9-8=1

а₁=(3+1)/2=2 log₅x = 2 х₁=5²=25

а₂=(3-1)/2=1 log₅x = 1 х₂=5¹=5

1 votes Thanks 1

ggggraanat Спасибо большое)

MizoriesKun ))

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