A term that contains a logarithmic expression is called a logarithmic term.

Any quantity can be expressed in logarithmic form. If a quantity is expression in the form a term and it contains a logarithmic form expression, then the term is called a logarithmic term.

For example, $3$ is a number. It can be expression in logarithmic form.

$3 \,=\, \log_{2}{8}$

Mathematically, the term $\log_{2}{8}$ can be written instead of $3$.

Basically, logarithm of $8$ to the base $2$ is a term and it represents a number. Moreover, the term is in the logarithmic form. Hence, the term $\log_{2}{8}$ is called a logarithmic term.

Logarithmic terms are formed in three different types possibly.

01

Only a single logarithmic term represents the quantity completely.

$(1) \,\,\,\,\,\,$ $\log_{3}{10}$

$(2) \,\,\,\,\,\,$ ${(\log_{6}{1898})}^4$

$(3) \,\,\,\,\,\,$ $\log_{e}{91}$

$(4) \,\,\,\,\,\,$ $\log_{a}{b^2}$

$(5) \,\,\,\,\,\,$ $\log_{xy}{(1+xyz)}$

02

The terms are also formed by the product of numbers and logarithmic form expressions. Due to the involvement of the logarithmic form expressions, the terms are called logarithmic terms.

$(1) \,\,\,\,\,\,$ $5\log_{2}{7}$

$(2) \,\,\,\,\,\,$ $-8{(\log_{4}{190})}^2$

$(3) \,\,\,\,\,\,$ $0.78\log_{e}{11211}$

$(4) \,\,\,\,\,\,$ $b\log_{c}{ac^3}$

$(5) \,\,\,\,\,\,$ $(2+x^2)\log_{z}{(1-x^2)}$

03

The terms are also formed in division form to represent quantities by their quotients. If a term contains, a logarithmic form expression, then it is known as a logarithmic term.

$(1) \,\,\,\,\,\,$ $\dfrac{-7}{\log_{5}{3}}$

$(2) \,\,\,\,\,\,$ $\dfrac{{(\log_{12}{50})}^7}{10}$

$(3) \,\,\,\,\,\,$ $\dfrac{5}{0.9\log_{e}{(7g)}}$

$(4) \,\,\,\,\,\,$ $\dfrac{\log_{10}{(xyz)}}{z^2}$

$(5) \,\,\,\,\,\,$ $\dfrac{1-b}{\log_{b}{(1-ab^8)}}$