Unlike logarithmic terms

Definition

The logarithmic terms which do not contain same logarithmic coefficient are called unlike logarithmic terms.

In some cases, the logarithmic part in a logarithmic term does not match with the logarithmic part of another logarithmic term and it can be true in the case of two or more logarithmic terms. In this case, the logarithmic terms are appeared dissimilarly due to involvement of different logarithmic coefficients. Hence, the logarithmic terms are called unlike logarithmic terms mathematically.

Examples

Study the following examples to understand how to identity the unlike logarithmic terms mathematically.

$(1) \,\,\,$ $6\log_{3}{7}$ and $4\log_{4}{10}$

$6$ and $4$ are numerical coefficients. $\log_{3}{7}$ and $\log_{4}{10}$ are the logarithmic coefficients and compare both of them. They are not like. So, they are unlike. Therefore, the logarithmic terms are called unlike logarithmic terms.

$(2) \,\,\,$ $-7\log_{8}{5}$ and $4\log_{8}{6}$

In this example, $-7$ and $4$ are the numerical coefficients. $\log_{8}{5}$ and $\log_{8}{6}$ are logarithmic coefficients. In this case, the bases of them is same but the numbers are different. So, they are dissimilar. Hence, the logarithmic terms are unlike logarithmic terms.

$(3) \,\,\,$ $-9\log_{2}{41}$, $-9\log_{3}{51}$ and $-9\log_{4}{61}$

$-9$ is a common numerical coefficient in all three terms. $\log_{2}{41}$, $\log_{3}{51}$ and $\log_{4}{61}$ are the logarithmic coefficients. In this case, numerical coefficients are same but logarithmic coefficients are different. Therefore, the logarithmic terms are known as unlike logarithmic terms.

Remember, the numerical coefficient or any other coefficient is not considered to determine the unlike logarithmic terms but logarithmic coefficients are only considerable factor to determine the unlike logarithmic terms.


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