решите, что сможете пожалуйста

1) log15 75 = log15 (5*15) = log15 5 + log15 15 = 1/log5 15 + 1 =
= 1 / (log5 (3*5) +1 = 1 / [log5 3 + log5 5] + 1 =
= 1 / log3 5 + 1) + 1
___ log2 5 = a
___ log2 3 = b
=>
log2 5 / log2 3 = a / b
log3 5 = a/b
=>
1 / (log3 5 + 1) + 1 =
= 1 / ((a/b) + 1) + 1 =
= 1 / [(a+b)/b] + 1 =
= b / (a+b) + 1 =
= (b + a + b) / (a + b) =
= (2b + a) / (a + b)
2)
log2 (4x-3) + log(1/8) 125 = log(0,5) x + log4 0,04
ОДЗ: (4x-3) > 0 и x > 0 или
x > 3/4 и x > 0 --------------------> x > 3/4
___ log(1/8) 125 = log{2^(-3)} 5^3 = 3/(-3) * log2 5 = - log2 5
___ log(0,5) x = log{2^(-1)} x = 1/(-1) * log2 x = - log2 x
___ log4 0,04 = log(2^2) 0,04 = 1/2 * log2 0,04 = log2 0,04^(1/2) = log2 0,2
=>
log2 (4x-3) + (- log2 5) = (- log2 x) + log2 0,2
log2 (4x-3) - log2 5 = log2 0,2 - log2 x
log2 [(4x-3)/5] = log2 [0,2/x]
(4x-3)/5 = 0,2/x
x*(4x-3) = 1
4x^2 - 3x - 1 = 0
x1 = -1/2 - не удовлетворяет ОДЗ.
x2 = 8
=> ответ: x = 8
Плохо видно дальше