Question

1)given that log(y)/log(4)=a and log(2y)/log(8)=b, show that 2a=3b-1

2)the strength (S) of an earthquake is represented by ritcher scale (R) and the relationship is as follows:
R=log(S)/log(10).show that when the ritcher scale shows an increase in value by 1,the strength of the earthquake will have increased by 10 times.

Answer 1

Note that log_2(n) = 2*log_4(n) = 3*log_8(n)

a = log_4(y) = (1/2) log_2(y)
b = log_8(2y) = log_8(2) + log_8(y) = 1/3 + (1/3) log_2(y)

b = 1/3 + (2/3) a
3b = 1+2a

If logn = logm + 1,
logn = logm + log10 = log(10m)

so, n = 10m