Laws of Logarithms and Change of Base

Logarithm study has a few formulas that are important and key to solving math questions. By remembering them, you will be in line to solve logarithmic problems and, maybe, fast too. There are a few logarithms laws that are formed by combining two logs of the same base. 

• Product rule :  log(ab) = log(a) + log(b)
• Quotient rule : log(a/b) = log(a) - log(b)
• Power rule : log(xⁿ) = nlog(x)                     Ex: log₃9² = 2log₃9

If the logarithm to the base a is known, then the logarithm to the base b can be obtained by the base change relationship:

, b>0, b≠1, x>0

The base change formula helps in evaluating logarithms or graphing log functions with any base. For graphing, first find the inverse of the function in exponential form and draw its graph. To draw the graph of the function, reflect in the line y=x.