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.

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

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

$(3) \,\,\,\,\,\,$ $\dfrac{5}{0.9\log_{e}{(7g)}\log_{2}{h}}$

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

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

Latest Math Topics

Apr 18, 2022

Apr 14, 2022

Apr 05, 2022

Mar 18, 2022

Mar 05, 2022

Latest Math Problems

Apr 06, 2022

Mar 22, 2022

A best free mathematics education website for students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Learn how to solve the maths problems in different methods with understandable steps.

Copyright © 2012 - 2021 Math Doubts, All Rights Reserved