1)
log₀,₈ (1+2x)=log₀,₈ (4x-10)
ОДЗ:
{1+2х > 0 {x>-0,5
{4x-10>0 {x>2,5 => x>2,5
1+2x = 4x-10
2x-4x = -1-10
-2x = -11
x = (-11) : (-2)
x = 5,5
Ответ: х= 5,5
2) log₂ (х-6)+log₂ (х-8)=3
ОДЗ:
{x-6 > 0 {x>6
{x-8>0 {x>8 => x>8
log₂(х-6)(х-8) = 3
(х-6)(х-8) = 2³
(х-6)(х-8) = 8
х²-6х-8х+48=8
х²-14х+48-8=0
х²-14х+40=0
D = b² - 4ac
D = 196 - 4·1·40 = 196 - 160 = 36
√D = √36 = 6
x₁ = (14-6)/2 =8/2 = 4 - посторонний корень, т.к. не удовлетв. ОДЗ
x₂ = (14+6)/2 =20/2 = 10
Ответ: х=10