Cambridge IGCSE Additional Mathematics · Syllabus 0606 · Logarithmic and Exponential Functions
Laws of Logarithms
What is Laws of Logarithms?
The three rules that convert operations inside a logarithm into simpler operations outside it, valid for a base a with a greater than zero and a not equal to one and for strictly positive arguments M and N. The product law says the logarithm of M times N equals the logarithm of M plus the logarithm of N. The quotient law says the logarithm of M divided by N equals the logarithm of M minus the logarithm of N. The power law says the logarithm of M raised to the power k equals k times the logarithm of M. All three are index laws in disguise, because a logarithm is an exponent, and none of them applies to a sum: the logarithm of M plus N cannot be split.
This definition is part of the Logarithmic and Exponential Functions chapter in Cambridge IGCSE Additional Mathematics.