Manipulation of Logarithms

With Logarithms, there aren't that many ways that they can manipulated. Here are the 6 different rules that will allow you to manipulate most equations:

Where 'b' is the base
Where 'a' is the part in the brackets

1)  The log can be manipulated  to remove the log if it is given a value: here such as 'c'.

Logb(a)=z       Then b^z=a

2)  The Coefficient of the Log can be moved to the power:

Y Logb(a) = Logb(a)^Y

3)  The Log of (ac) can be written as two different Logs; where they are split by an addition sign.

Logb(as) = Logb(a) + Logb(s)

4) The Division of the Log can be changed to a minus sign, keeping the base of the log the same.

Logb(a/s) = Logb(a) - Logb(s)

5) Any Log with the base the same as the part in the brackets will = 1. This is because anything to the power of 1 will equal itself. 

Logb(b) = 1

6) When changing the base of the Log: Rewrite the same thing but change the base to whatever you want; then divide this by Log with the new base, with in brackets the old base.

Where c is the new base

Logb(a) = Logc(a)/Logc(b)