$log_{(.001)} (100)$ = ?

For Competitive Exams

$\dfrac{-2}{3}$

$\dfrac{3}{2}$

$\dfrac{-3}{2}$

None of these

Explanation:

Let $log_{(.001)} (100)$ =p

$(.001)^p$=100

$\left(\dfrac{1}{1000}\right)^p$=100

$\left(\dfrac{1}{10^3}\right)^p$=$10^2$

$[\left(10\right)^{-3}]^p$=$10^2$

$\left(10\right)^{-3p}$=$10^2$

-3p=2

p=$\dfrac{-2}{3}$

Next Question

$(log_{3} 4)$ $(log_{4} 5)$ $(log_{5} 6)$ $(log_{6} 7)$ $(log_{7} 8)$ $(log_{8} 9)$$ (log_{9} 9)$ = ?

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