Bài 1 :
a) 2 . 3^x = 10 . 3^{12} + 8 . 27^4
=> 2 . 3^x = 10 . 3^{12} + 8 .3^{12}
=> 2 . 3^x = 3^{12} . (10 + 8)
=> 2 . 3^x = 3^{12} . 18
=> 3^x = 3^{12} . 18 : 2
=> 3^x = 3^{12} . 3^2
=> 3^x = 3^{14}
=> x = 14
Vậy x = 14
b) 2 . 3^{x + 1} - 3^x = 135
=> 2 . 3^x . 3 - 3^x = 135
=> 3^x . (2.3 - 1) = 135
=> 3^x . 5 = 135
=> 3^x = 135 : 5
=> 3^x = 27
=> 3^x = 3^3
=> x = 3
Vậy x = 3
c) 15 : (x + 2) = 3^3 + 3 : 10
=> 15 : (x + 2) = 27 + 3/10
=> x + 2 = 15/(27 + 3/10)
=> x + 2 = 50/91
=> x = 50/91 - 2
=> x = -132/91
Vậy x = -132/91
d) 4(3x - 1)^3 - 5^2 = 475
=> 4(3x - 1)^3 - 25 = 475
=> 4(3x - 1)^3 = 475 + 25
=> 4(3x - 1)^3 = 500
=> (3x - 1)^3 = 500 : 4
=> (3x - 1)^3 = 125
=> (3x - 1)^3 = 5^3
=> 3x - 1 = 5
=> 3x = 6
=> x = 2
vậy x = 2
Bài 2 :
a) 2^x + 2^{x + 1} = 96
=> 2^x + 2^x . 2 = 96
=> 2^x . (1 + 2) = 96
=> 2^x . 3 =96
=> 2^x = 96 : 3
=> 2^x = 32
=> 2^x = 2^5
=> x = 5
Vậy x =5
b) 3^{8x + 4} = 81^{x + 3}
=> 3^{8x + 4} = (3^4)^{x + 4}
=> 3^{8x + 4} = 3^{4x + 16}
=> 8x + 4 = 4x + 16
=> 8x - 4x = 16 - 4
=> 4x = 12
=> x = 3
vậy x = 3
c) x^{2015} = x^{2016}
=> x^{2015} - x^{2016} = 0
=> x^{2015} . (1 - x) = 0
@ TH1 : x^{2015} = 0
=> x = 0
@ TH2 : 1 - x = 0
=> x = 1
Vậy x = 0 hoặc x = 1
d) (4x - 1)^3 = 27 . 125
=> (4x - 1)^3 = 3375
=> (4x - 1)^3 = 15^3
=> 4x - 1 = 15
=> 4x = 16
=> x = 4
vậy x =4
