Уравнения по математике

{2^(6x+3)=2^5*2^(4y-1)
{5*5^(x-y)=5^(2y+1)

{2^(6x+3)=2^(4y+4)
{5^(x-y+1)=5^(2y+1)

{6x+3=4y+4
{x-y+1=2y+1

{6x-4y=1
{x-3y=0
x=3y
6*3y-4y=1
14y=1
y=1/14
x=3/14
(3/14;1/14)

2)
{ 2*log4 x + log2 (y-1) = 1 -----------> ОДЗ: x>0 и y>1
{ log8 x * log(V2) (y-1) = - 4\3
=>
___ 2*log4 x = 2*(log(2^2) x = 2 * (1\2) * log2 x = log2 x
___ log8 x = log(2^3) x = (1\3) * log2 x
___ log(V2) (y-1) = log(2^(1\2) (y-1) = (1\(1\2) * log2 (y-1) = 2*log2 (y-1)
=> получится система:
{ log2 x + log2 (y-1) = 1
{ 1\3 * log2 x * 2 * log2 (y-1) = - 4\3 -------------------------> log2 x * log2 (y-1) = - 2
=> замена ----------> log2 x = a ---и ------> log2 (y-1) = b =>
{ a + b = 1 -----------> { b = 1 - a
{ a * b = - 2 -------> { a * (1 - a) = - 2
=>
a - a^2 = - 2
a^2 - a - 2 = 0 ---> a1 = -1; a2 = 2 и b1 = 1-a1 = 2; b2 = 1 - a2 = 1-2 = -1
a1 = -1 ------> b1 = 2
a2 = 2 -------> b2 = -1
a1 = -1 ----> log2 x = a1 = -1 -----------------------------------------> x1 = 2^(-1) = 1\2
a2 = 2 -----> log2 x = a2 = 2 -------------------------------------------> x2 = 2^2 = 4
b1 = 2 -----> log2 (y-1) = b1 = 2 -----> (y-1) = 2^2 ----------------> y1 = 5
b2 = -1 ----> log2 (y-1) = b2 = -1 -----> (y-1) = 2^(-1) = 1\2 -----> y2 = 3\2
=>
x1 = 1\2 -----> y1 = 5
x2 = 4 --------> y2 = 3\2