8th Class Mathematics Logarithms Question Bank Logarithms

  • question_answer If \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{a}}}\mathbf{(ab)=x,}\] then \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{b}}}\](ab) is:

    A)  \[\frac{1}{x}\]                         

    B)  \[\frac{x}{x+1}\]

    C)  \[\frac{x}{1-x}\]                       

    D)  \[\frac{x}{x-1}\]

    Correct Answer: D

    Solution :

    (d): \[lo{{g}_{a}}(ab)=\Leftrightarrow \frac{logab}{\log a}=x\Leftrightarrow \frac{loga+logb}{\log a}\text{ }=x\] \[\Leftrightarrow 1+\frac{\log b}{\log a}=x\Leftrightarrow \frac{\log b}{\log a}=x-1\] \[\Leftrightarrow \frac{\log a}{\log b}=\frac{1}{x-1}\Leftrightarrow 1+\frac{\log a}{\log b}=1+\frac{1}{x-1}\] \[\Leftrightarrow \frac{\log b}{\log b}+\frac{\log a}{\log b}=\frac{x}{x-1}\,\,\,\Leftrightarrow \frac{\log b+\log a}{\log b}=\frac{x}{x-1}\] \[\Leftrightarrow \frac{\log (ab)}{\log b}=\frac{x}{x-1}\,\,\,\Leftrightarrow {{\log }_{b}}(ab)=\frac{x}{x-1}\]

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