#1
log 4 64 + 2log 5 1/25 + log 16 2 = log 4 4^3 + 2 log 5 5^-2 + log 2^4 2 = 3log 4 4 + 2 * (-2) log 5 5 + 1/4 log 2 2 = 3*1 - 4*1 + 1/4 * 1 = 3 - 4 +1/4 = -1 + 0.25 = -0.75
#3
a) 6^(4x+7) = 1/216
6^(4x+7) = 6^-3
4x+7 = -3
4x = -10
x = - 10/4
x = -2.5
б) log 3-x (3x^2 - 8x +5) =2
log 3-x (3x^2 - 8x +5) = log 3-x (9 - 6x+ x^2)
3x^2 - 8x +5 = x^2 -6x + 9
2x^2 - 2x - 4=0
x^2 - x -2=0
D = 1 - 4*1*(-2) = 9
x1 = (1+3)/2 = 2
x2 = (1-3)/2 = -1
в) lg(5x-4) - lg (2 + 7x) = 0
lg(5x-4) = lg (2 + 7x)
5x-4 = 2+7x
2x = -6
x = -3