From the introduction to logarithm, we know that the value of a logarithm does not make any sense without the base. In the topic of logarithms, we often hear the terms common logarithm and natural logarithm. In this section, we will discuss them. Common Logarithm The logarithm of a number with base 10 is called the common logarithm … Read more
We will use the following formulas to solve the problems of logarithms. • Product Rule of Logarithm: $\log_a(MN)=\log_a M +\log_a N$ • Quotient Rule of Logarithm: $\log_a(M/N)=\log_a M -\log_a N$ • Power Rule of Logarithm: $\log_a M^k=k\log_a M$ • Base Change Rule of Logarithm: $\log_a M=\log_b M \cdot \log_a b$ Problem 1: Find the value of … Read more
For the basic concepts of the logarithm, we refer to our page “an introduction to logarithm”. To express the power of a number, we use the concept of the logarithm. Note that $a^x=b$ can be written in the logarithmic language as follows: $x=\log_a b.$ Moreover, \[a^x=b \text{ if and only if } x=\log_a b.\] In … Read more
A logarithm is used to express any power of a number. In this section, we will learn about logarithms with examples and properties. Definition of Logarithm For $a>0, a\neq 1$ and $M>0,$ assume that $a^x=M.$ In this case, the number $x$ is said to be the logarithm of $M$ with respect to the base $a,$ … Read more