В этих примерах используются свойства логарифмов, а именно:
a^(loga(b)) = b
loga(b^c) = c*loga(b)
log(a^c) (b) = (1/c)*loga(b)
loga(a) = 1
1033. 16^(log4(13)) = 4^(2log4(13)) = 4^(log4(13^2)) = 13^2 = 169
1034. 64^(log8(7)) = 8^(2log8(7)) = 7^2 = 49
1035. log9(22) / log81(22) = log9(22) / 0.5*log9(22) = 2
1036. log5(5)/log16(5) = 1/log16(5) = log5(16) = 4log5(2)
Cos(x+pi/5)=√3sin(x+pi/5),
cos(x+pi/5)/sin(x+pi/5)=√3,
ctg(x+pi/5)=√3,
x+pi/5=pi/6+pi*k, k-целые,
x=pi/6-pi/5+pi*k,
x= -pi/30 +pi*k, k-целые
0+2arcsin(-√3/2)-arcsin1/2
2*(-p/3)-(p/6)
(-2p/3)-(p/6)
-5p/6
(a+2)(a-8)-2a(a-3)=а^2-8а+2а-16-2а^2+6а=-а^2
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2 5
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x ∈ [5 ; + ∞)
Ответ: 5