tentukan himpunan penyelesaian dari persamaan persamaan logaritma berikut : A. ^3log (x-5)-^3log(18-2x)=0 B. ^3log(x+4)=^9log(26-x^2) C. ^3log^2^3logx-8=0

jawab

A. 
3'log (x - 5)  = 3'kog (18-2x)
x - 5 = 18 - 2x
3x = 23
x = 23/3

B.
3'log (x + 4) = 9'log (25 - x^2)
3'log ( x+ 4) = 3'log (25 - x^2 )^(1/2)
x+ 4 = √(25 - x^2)
(x+4)² = 25 - x²
x² + 8x + 16 + x²-25 = 0
2x² + 8x - 9 = 0
x²+ 4x -9/2 =0
x² + 4x  =  9/2
(x + 2)² = 9/2 + 4 = 17/2
x + 2 = +- √(17/2)
x = - 2 + 1/2 √ 34

c.
3'log²  (3'log x)  - 8 = 0

misal 3'log x = a
3'log² (a) =8
3'log a = √8
a = 3^(√8)

3'log x = a
x = 3^a
x = 3^(3^(√8))

LogAritMa

•
³log (x - 5) - ³log (18 - 2x) = 0
x - 5 = 18 - 2x
x + 2x = 18 + 5
x = 23/3

••
3'log (x + 4) = 9'log (26 - x²)
2 . 9'log (x + 4) = 9'log (26 - x²)
(x + 4)² = 26 - x²
x² + 8x + 16 + x² - 26 = 0
2x² + 8x - 10 = 0
x² + 4x - 5 = 0
(x + 5)(x - 1) = 0
x = -5 atau x = 1

Nilai x yg memenuhi :
x = 1

•••
³log² (³log x - 8) = 0
³log x - 8 = 1
³log x = 1 + 8
x = 3^9

^ baca pangkat