вправа 6.22 гдз 11 клас алгебра Істер 2019
Вправа 6.22
Розв'яжіть рівняння:
1) log2(3log2х + 1) = 2;
2) log9(log2(log√3х)) = 1/2.
1) log2(3log2х + 1) = 2;
2) log9(log2(log√3х)) = 1/2.
Умова:
Відповідь:
1) log2(3log2х + 1) = 2
ОДЗ: х > 0
3log2х + 1 = 22
3log2х + 1 = 4
3log2х = 3
log2х = 1
х = 2;
2) log9(log2(log√3х)) = 1/2
ОДЗ: х > 0
log2(log√3х) = 91/2
log2(log√3х) = 3
log√3х = 23
log√3х = 8
log31/2х = 8
1/(1/2)log3х = 8
2log3х = 8
log3х = 4
х = 34
х = 81.
ОДЗ: х > 0
3log2х + 1 = 22
3log2х + 1 = 4
3log2х = 3
log2х = 1
х = 2;
2) log9(log2(log√3х)) = 1/2
ОДЗ: х > 0
log2(log√3х) = 91/2
log2(log√3х) = 3
log√3х = 23
log√3х = 8
log31/2х = 8
1/(1/2)log3х = 8
2log3х = 8
log3х = 4
х = 34
х = 81.