We always heard about the logarithms log and ln. So it is important to know about their meaning and differences. Note that log represents the common logarithm and ln represents the natural logarithm. In this post, we will learn about them. What is log? The notation log is referred to the short form of the … Read more
In this section, we will solve problems on logarithms. For the definition of a logarithm, please click on this link. At first, we will recall the main formulas of logarithms: Formula 1: $\log_a(MN)=\log_a M + \log_a N$ Formula 2: $\log_a(M/N)=\log_a M – \log_a N$ Formula 3: $\log_a M^n=n \log_a M$ Formula 4: $\log_a M=\log_b M … Read more
From the Introduction to logarithm, we know that the value of a logarithm is meaningless if we do not mention the base. Definition of Common Logarithm The logarithm with base 10 is called the common logarithm. This is also known as the decimal logarithm. For example, log105, log107 are the common logarithms of 5 and … Read more
Here we learn the general laws of logarithms. The list of logarithm formulas are given at the end of this post. Proofs of Logarithm Formulas: Proof of Product Rule of logarithms loga(MN)=loga M + loga N Proof: Suppose that x= loga M Thus, by the definition of logarithm ax=M Again, suppose that y=loga N ⇒ … Read more
In this section, we will learn about logarithms with examples and properties. Definition of Logarithm We consider $a>0, a \ne 1$ and $M>0$, and assume that ax =M. In this case, we will call $x$ to be the logarithm of $M$ with respect to the base $a$. We write this phenomenon as x= loga M … Read more