1. log15(75) = log2(15)/log2(75) = (log2(5) + log2(3))/(log2(5) + log2(5) + log2(3)) = (a + b)/(2a + b).
2. a.
–log3(3x – 2) + log3(0.25) = log3(x) – (1/3)log3(64),
log3(0.25/(3x – 2)) = log3(x/4),
0.25/(3x – 2) = x/4,
x = 1.
2. b.
(log2(4 – x))^2 + log2(4 – x) – log2(8) = (2^log2(9))^(1/2),
log2(4 – x) = t.
t^2 + t – 3 = 3,
t^2 + t – 6 = 0
t = –3 или t = 2.
log2(4 – x) = –3 или log2(4 – x) = 2.
x = 0 или x = 31/8.
3.
7^log5(x) > (7/3)^log5(5x-6)
7^log5(x)*3^log5(5x-6) > 7^log5(5x-6),
5x - 6 > 0,
x > 6/5.