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Class 9
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Math
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Logarithms
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Formulas / Equations

Logarithms

Formulas / Equations

Math

  1. log⁡a(mn)=log⁡am+log⁡an​\log a{(mn)}=\log_am+\log _an​loga(mn)=loga​m+loga​n​

    When taking logarithm of two or more terms multiplying together, use this formula to further solve the logarithm. For Example:

    log⁡(4.3×3.7×23.5)\log({4.3\times 3.7\times 23.5})log(4.3×3.7×23.5)

    log⁡4.3+log⁡3.7+log⁡23.5\log{4.3}+\log{3.7}+\log{23.5}log4.3+log3.7+log23.5

    In simple words the logarithm of the product of two or more numbers is equal to the sum of the logarithm of the numbers.

  2. log⁡a(mn)=log⁡am−log⁡an​\log a{(\frac{m}{n})}=\log am-\log _an​loga(nm​)=logam−loga​n​
    When taking logarithm of two or more terms dividing each other, use this formula to further solve the logarithm. For Example:

    log⁡(32.5456.5)\log{(\frac{32.5}{456.5})}log(456.532.5​)

    log⁡32.5−log⁡456.5\log{32.5}-\log{456.5}log32.5−log456.5

    In simple words the logarithm of the quotient of two or more numbers is equal to the difference of the logarithm of the numbers.

  3. log⁡a(mn)=nlog⁡am\log a{(m^n)}=n\log amloga(mn)=nlogam
    When taking logarithm of a term that has an exponent (power) on it, use this formula to further solve the logarithm. For Example:

    log⁡(43.7)12\log(43.7)^\frac{1}{2}log(43.7)21​

    12(log⁡43.7)\frac{1}{2}(\log{43.7})21​(log43.7)

    In simple words the logarithm of a number that has an exponent is equals to the the product of the power and the logarithm of the number.

  4. log⁡a(n)=log⁡bnlog⁡ba\log a{(n)}=\frac{\log bn}{\log _ba}loga(n)=logb​alogbn​

    When taking logarithm of a number with a specific base of logarithm and there is a need of changing that base. Use this formula to change the base.

    For Example:

    log⁡5(568.9)\log_5(568.9)log5​(568.9)

    log⁡(568.9)log⁡(5)\frac{\log (568.9)}{\log (5)}log(5)log(568.9)​

    Here the base is now simple common logarithm base which is 10.


    Note: Since in exams scientific calculator is not allowed and if this kind of question appear one would not be able to solve it. Thus use this formula to solve this kind of question furthermore.