A term that represents a quantity in logarithmic form is called a logarithmic term. It can also be simply called as a log term.
Any quantity can be expressed in logarithmic form. If the quantity is written as a term in logarithmic form then the term is known as a logarithmic term.
$3$ is a number. It can be written in logarithmic form as follows.
$3 \,=\, \log_{2}{8}$
Mathematically, the term $\log_{2}{8}$ represents the quantity $3$ and moreover, it is in logarithmic form. Therefore, the term $\log_{2}{8}$ is called as a logarithmic term, or simply a log term.
Logarithmic terms are formed in four different ways possibly.
Every real number can be expressed in logarithmic form. So, just consider every real number as a logarithmic term.
Only a single logarithmic term represents the quantity completely.
$(1) \,\,\,\,\,\,$ $\log_{3}{10}$
$(2) \,\,\,\,\,\,$ ${(\log_{6}{1898})}^4$
$(3) \,\,\,\,\,\,$ $\log_{e}{91}$
$(4) \,\,\,\,\,\,$ $\log_{a}{b^2}$
$(5) \,\,\,\,\,\,$ $\log_{xy}{(1+xyz)}$
The product of two or more quantities is also a quantity. So, a term can be a product of two or more quantities in which at least a quantity can be in logarithmic form. The terms are called as log terms in such cases.
$(1) \,\,\,\,\,\,$ $5\log_{2}{7}$
$(2) \,\,\,\,\,\,$ $-8{(\log_{4}{190})}^2$
$(3) \,\,\,\,\,\,$ $0.78\log_{e}{11211}$
$(4) \,\,\,\,\,\,$ $b\sin{(d^2)}\log_{c}{ac^3}$
$(5) \,\,\,\,\,\,$ $(2+x^2)\log_{z}{(1-x^2)}$
The quotient of two quantities is also a quantity. So, a term is also quotient of quantities in which at least a quantity can be in log form, then the terms are called as log terms mathematically.
$(1) \,\,\,\,\,\,$ $\dfrac{-7}{\log_{5}{3}}$
$(2) \,\,\,\,\,\,$ $\dfrac{{(\log_{12}{50})}^7}{10}$
$(3) \,\,\,\,\,\,$ $\dfrac{5}{0.9\log_{e}{(7g)}\log_{2}{h}}$
$(4) \,\,\,\,\,\,$ $\dfrac{\log_{10}{(xyz)}}{z^2}$
$(5) \,\,\,\,\,\,$ $\dfrac{1-b}{\log_{b}{(1-ab^8)}}$
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