if a,b,c are in a G P ,prove that log a,log b,log c are in an A P - Maths - Sequences and Series

Question

if a,b,c are in a G P ,prove that log a,log b,log c are in an A
P

S. Usha Rani · Accepted Answer

if a , b and c are in GP so b2 = ac
b/a = c/b ---------- (A)
now
log a - log b = log a/b
and according to equation (A)
log b/a = log c/b
means
log b - log a = log c - log b
2 log b = log a + log c
Hence they are in A P

if a,b,c are in a G.P ,prove that log a,log b,log c are in an A.P.