Помогите решить показательные уравнения

1) 6^(х-2) - 6^(х-1) = -180
6^(х-2) × (1-6) = -180
6^(х-2) × -5 = -180
6^(х-2) = 36
6^(х-2) = 6^2
х-2=2
х=4

2) 2×4^х - 15×2^х - 8 = 0
2×2^2х - 15×2^х - 8 = 0
а = 2^х, а>0
2а² - 15а - 8 = 0
D = 17²
а1 = (15+17)/4 = 8
а2 = (15-17)/4 = -0,5 -> не принадлежит условию а>0
2^х = 8
2^х = 2^3
х = 3

3) 5×(1/2)^(х-3) + (1/2)^(х+1) = 162
(1/2)^(х-3) × (5 + (1/2)⁴) = 162
(1/2)^(х-3) × (81/16) = 162
(1/2)^(х-3) = 32
(1/2)^(х-3) = (1/2)^(-5)
х-3=-5
х=-2

4) 4^(х-1) - 6^(х-1) = 0
4^(х-1) = 6^(х-1)
(4/6)^(х-1) = (4/6)^0
х-1=0
х=1

5) 2^(х²-3) × 5^(х²-3) = 0,01(10^(х-1))³
10^(х²-3) = 10^(3х-5)
х² - 3= 3х - 5
х² - 3х + 2 = 0
D = 1
х1=2
х2=1

1) 6^(x-2) (1 - 6) =-180
6^(x-2)=36
x-2 = 2
x=4

2) 2^x= t, t >0
2t^2 -15 t -6 =0
t1= 8, 2^x = 2^3 = . x= 3
t2 < 0 - не подх

3) (1/2)^:(x-3) * ( 5 +(1/2)^4) = 162
(1/2)^:(x-3) * ( 81/16) = 162
(1/2)^:(x-3) = 32
2^ (3-x) = 2^5
3-x = 5 = > x = -2

4) 4 ^(x-1) = 6 ^(x-1)
(2/3) ^ (x-1) = 1
x-1 = 0 = > x= 1

5) 10^( x^2 -3) = 10^(3x -5)....