1. The sequence log2 32, log2 y, log2 128, ... forms an arithmetic sequence. What is the value of y?

Question

2. If log a^2 b^3 = x and log (a/b) = y, what are the values of log a and log b?

Answer 1

128/32 = r^2
r=2, so y=32*2=64
Or, evaluate the logs. The sequence is thus
5,log2(y),7
so, log2(y) = 6, and y=64

log a^2b^3 = 2loga + 3logb
log a/b = loga - logb

2loga + 3logb = x
loga - logb = y

2loga + 3logb = x
2loga - 2logb = 2y
5logb = x-2y
logb = (x-2y)/5

solve for loga in like wise.