Question

Алгебра Логарифмы, помогите пожалуйста))

Answer 1

1) 
a) log(2) 256 = log(2) (2^8) = 8*log(2) 2 = 8
б) log(3) (1/27) = -3*log(3) 3 = - 3
в) log(7) (√7) = 1/2
д) log(1/3) (1/2187) = log(1/3) (1/3)^7 = 7
е)  log(1/4) 256 = - log(4) 4^4 = 4
ж)  log(0,5)  (0,0625) = log(0,5) (0,5)^4 = 4
з)  lg   (10000) = lg (10)^4 = 4
и)  log(3/4)  (3/4) = 1
к)  log(256) 4 = 1/4
г) log(155) 1 = 0
д) (log(4) 102)/log(4)^4 102 = 4 
2) а)  2/5
б) 5^3 / (5^(log(5) 0,8) = 15/0,8 = 18,75
в)  log(3) (2*13,5) = log(3) 27 = 3
г)  log(1/5) (6/750) = log(1/5) (0,008)= log(0,2) (0,2)^3 = 3

3)  а) log(π) x = 0
x = π^0 = 1
б) log(x) 2 = -1/5
x^(/-1/5) = 2
x = 1/32
в)  x^2 - 4x + 20 = (1/2)^(-5)
x^2 - 4x + 20 = 32
x^2 - 4x + 12 = 0
x1 = 6
x2 = - 2