Like logarithmic terms

Definition

The logarithmic terms which contain same logarithmic coefficient are called like logarithmic terms.

In some cases, the logarithmic part of a logarithmic term is matched with the logarithmic part of another logarithmic term. It can be true in two or more logarithmic terms. Due to the involvement of a same logarithmic form expression in forming the logarithmic terms, the logarithmic terms are appeared similarly. Hence, the logarithmic terms are called like logarithmic terms mathematically.

Examples

Examine the following examples to identity the like logarithmic terms.

$(1) \,\,\,$ $6\log_{3}{7}$ and $-8\log_{3}{7}$

In this example, $6$ and $-8$ are numerical coefficients but they both have $\log_{3}{7}$ as a logarithmic coefficient commonly. Due to the common logarithmic coefficient, the logarithmic terms $6\log_{3}{7}$ and $-8\log_{3}{7}$ are called the like logarithmic terms.

$(2) \,\,\,$ $d\log_{a}{xy}$, $\Big(\dfrac{1}{c}\Big)\log_{a}{xy}$ and $0.6\log_{a}{xy}$

In this example, $d$ and $\dfrac{1}{c}$ are literal coefficients and $0.6$ is the numerical coefficient. However, $\log_{a}{xy}$ is the common logarithmic coefficient in three logarithmic terms. Therefore, the three logarithmic terms are called like logarithmic terms.

Remember, logarithmic coefficient is the only considering factor while determining the like logarithmic terms and no need to consider numerical, literal or other coefficients. Therefore, just observe all the logarithmic terms, if two or more logarithmic terms have same logarithmic coefficient, then call them as like logarithmic terms.


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