Math: logarithms: exponent-to-multiple rule

Tutoring math, logarithms come up. The tutor mentions a way to see the exponent-to-multiple rule.

The following is by my understanding.

With logarithms – aka, logs – the log of a power can be made into a multiple of the log of that base. For instance,

log(a^b) = bloga.

Then again, the multiplication-to-addition rule says log(ab) = loga + logb.

The mutliplication-to-addition rule actually includes the exponent-to-multiple rule. For example:

log(4^3) = log(4*4*4) = log4 + log4 + log4 = 3log4

Source:

Travers,K.J., Dalton,L.C., Brunner,V.F., Taylor,A.R. (1977). Using Advanced Algebra. Doubleday Canada Limited.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.