Logarithm cancellation problem

Question

In a maths lecture recently, my tutor wrote that log base a of b multiplied by log base b of c was equal to log base a of c, apparently the b's in the equation cancel, however, I can't see any reason why they should, could you help me with this, thank you in advance.

Answer 1

your tutor used the change of base formula:

log(b)x=log(a)x/log(a)b

log(a)b*log(b)c=log(a)c

use the change of base formula on log(b)c

log(b)c=log(a)c/log(a)b

substitute

log(a)b*[log(a)c/log(a)b]=log(a)c

both log(a)b cancelled each other out leaving log(a)c