Question

If loga 2=logb 8,show that a^3=b.

Answer 1

Log[a] 2 = log[b] 8

log[a] 2 = log[b]2^3

log[a] 2 = 3log[b] 2

log[b] 2 = (log[a] 2)/(log[a] b)  <---- change of base

log[a] 2 = 3(log[a] 2)/(log[a] b)

3/(log[a] b) = 1

log[a] b = 3

a^3 = b