急 ! Logarithmic Function 9q13

33b) Suppose that M is the absolute magnitude of the Tangshan earthquake, then:

log M = 7.8

Thus, M/5 is the absolute magnitude of Tianjin Hangu aftershock, then in Ritcher Scale:

log (M/5) = log M - log 5 = 7.5

34a) log1/5 (a2b)/[log25 (a2b) + log25 (√b)]

= [(2 log a + log b)/(log 1/5)]/{[2 log a + log b + (1/2) log b]/log 25}

= [(2 log a + log b)/(-log 5)]/{[2 log a + log b + (1/2) log b]/(2 log 5)}

= - 2 (2 log a + log b)/(2 log a + log b)

= -2

b) log9 [(x2y)/3] - 2 log9 xy + log9 (y/3)

= 2 log9 x + log9 y - log9 3 - 2 log9 x - 2 log9 y + log9 y - log9 3

= - 2 log9 3

= -1