Tolong bantu jawab! Tentukan himpunan penyelesaian dari persamaan logaritma berikut A. 2 log x = 3 B. 2 log x + 2 log (2x-1)= 1

Kelas 10 Matematika
Bab Logaritma

^ = pangkat

1] ²log x = 3
x = 2^3
x = 8

HP = { 8 }

2] ²log x + ²log (2x - 1) = 1
²log (x . (2x - 1)) = ²log 2
2x² - x = 2
2x² - x - 2 = 0
a = 2; b = -1; c = -2

x12 = (-b +- √(b² - 4ac))/(2a)
x12 = (-(-1) +- √((-1)² - 4 . 2 . (-2)))/(2 . 2)
x12 = (1 +- √(1 + 16))/4
x1 = (1 + √17)/4

x2 = (1 - √17)/4

Syarat :
x > 0

2x - 1 > 0
2x > 1
x > 1/2

HP = { (1 + √17)/4 }