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)