№1
1) 7ˣ⁻¹ (7 - 1) = 6
7ˣ⁻¹ = 1
х - 1 = 0
х = 1
2) 3²ˣ⁻¹ + 3²ˣ⁻² - 3²ˣ⁻⁴ = 315
3²ˣ⁻⁴(3³ + 3² -1) = 315
3²ˣ⁻⁴ * 35 = 315
3²ˣ⁻⁴ = 9
2х - 4 = 2
2х = 6
х = 3
3) 5³ˣ⁻²(5² + 3) = 140
5³ˣ⁻² *28 = 140
5³ˣ⁻² = 5
3х - 2 = 1
3х = 3
х = 1
4) 2ˣ⁻¹(2² + 3 - 5*2) + 6 = 0
2ˣ ⁻¹ * (-3) = -6
2ˣ⁻¹ = 2
х - 1 = 1
х = 2
№2
1)log₂x - 2*log₂x/log₂2 = -1
log₂x - 2log₂x = -1
-log₂x = -1
log₂x = 1
x = 2
2) log₂x + log₂2/log₂x = 2,5|* log₂x
log₂²x + 1 = 2,5log₂x
log₂x = t
t² - 2,5t +1 = 0
t = 2 или t = 1/2
log₂x = 2 log₂x = 1/2
x = 4 x =√2
3) log₃x + 2*log₃3/log₃x = 3
log₃x +2/log₃x = 3 | * log₃x
log₃²x + 2 = 3log₃x
log₃x = t
t² - 3t + 2 = 0
t = 1 или t = 2
log₃x = 1 log₃x = 2
x = 3 x = 9
4) log₃x - 6*log₃3/log₃x = 1
log₃x - 6/log₃x = 1 | * log₃x
log₃²x - 6 = log₃x
log₃x = t
t² - t - 6 = 0
t = -2 или t = 3
log₃x = -2 log₃x = 3
x = 1/9 x = 27