Question

Tolong krjain, semoga kalian sukses

a. 2 4log ( x-1) = 1 + 4log ( x + 2 )

b. 3log . 3log x - 3log (2- 1/3 . 3log x) + 2

c. 6log 6x = 1 + 2x

Answer 1

A.
4'log(x-1)^2 = 4'log 4 + 4'log (x+2) 
(x-1)^2 = 4(x+2) dgn syarat x-1 > 0 atau x + 2 > 0--> x > 1
x^2 - 2x + 1 - 4x - 8 = 0
x^2 - 6x - 7 = 0
(x-7)(x+1) = 0
x = 7 atau x = -1 (TM)
HP x = 7
.
b) 3'log . 3'log x = 3'log (2 - 1/3. 3'log x) + 2
3'log . 3'log x = 3'log (2 - 1/3. 3'log x)(3^2)
3'log x = 9(2- 1/3. 3'log x)
3'log x = 18 - 3. 3'log x
4. 3'log x = 18
3'log x = 18/4 = 9/2
x = 3^(9/2) = √(3^8)(3) = 3^4 √3= 81√3 

.
c)  6'log 6x = 1+ 2x
6^(1+2x) = 6x
6. 6^(2x)= 6x
????
aneh

Answer 2

C. 6log 6x = 1 + 2x
   6log 6x = 6log 6^1+2x
         6x = 6^1+2x
         6x = 6 . 6^2x
           x = 6².6^x
           x = 36 . 6^x

a. 2 4log (x-1) = 1 + 4log (x+2)
       4log (x-1)² = 1 + 4log (x+2)
       4log (x-1)² = 4log 4 + 4log (x+2)
         (x-1)(x-1) = 4(x+2)
         x² - 2x + 1 = 4x + 8
         x² - 6x -7 = 0
       (x - 7)(x + 1) = 0
       *** x = 7, x= -1
b. 3log . 3log x = 3log (2- 1/3 . 3log x) + 2
   3log.3log x = 3log (2 - 1/3 . 3log x) + 3log 3²
         3log x = (2 - 1/3 . 3log x) . 3²
         3log x = (2/3 . 3log x ). 9
         3log x = 3log 3^(3log x ). 6
                x = 3^((3log x)(6))