Properties of Logarithm

First, a to the power of m in bracket times a to the power of in bracket equals a to the power of m plus n. Second, a to the power of m all over a to the power of n equals a to the power of m minus n. Third, Log b to the base of a equals n, so that b equals a to the power of n. Fourth, Log a to the base of g equals x, so that a equals g to the power of x. Fifth, Log b to the base of g equals y, so that g to the power of y.
Example:
What is the equivalence of Log a times b to the base of g?
Consequence Log a to the base of g equals x, so that a equals g to the power of x, and Log b to the base of g equals y, so that b equals g to the power of y. So a times b equals g to the power of x in bracket times g to the power of y equals g to the power of x plus y. So that Log a times b to the base of g equals Log g to the power of x plus y to the base of g equals x plus y in bracket times Log g to the base of g. If Log g to the base of g is one, so Log a times b to the base of g equals x plus y in bracket times one equals Log a to the base of g plus Log b to the base of g. So:
Log a times b to the base of g equals Log a to the base of g plus Log b to the base of g

What is the equivalence of Log a over b to the base of g?
Consequence a over b equals g to the power of x all over g to the power of y equals g to the power of x minus y. So than Log a over b to the base of g equals Log g to the power of x minus y to the base of g equals x minus y in bracket times Log g to the base of g equals x minus y in bracket times one equals Log a to the base of g minus Log b to the base of g. So:
Log a over b to the base of g equals Log a to the base of g minus Log b to the base of g