[2] (log_{3} 4) (log_{4} 5) (log_{5} 6) (log_{6} 7) (log_{7} 8) (log_{8} 9) (log

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TNPSC G4

10th CBSE Maths

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

Explanation:

$log_{3} 4\times log_{4} 5 \times log_{5} 6\times log_{6} 7 \times log_{7} 8 \times log_{8} 9 \times log_{9} 9$

$\dfrac{log \:4}{log\:3} \times \dfrac{log \:5}{log\:4} \times \dfrac{log \:6}{log\:5} \times \dfrac{log \:7}{log\:6} \times \dfrac{log \:8}{log\:7} \times \dfrac{log \:9}{log\:8} \times 1$

=$\dfrac{log \:9}{log\:3}$

=$\dfrac{log \:3^2}{log\:3}$

=$\dfrac{2log \:3}{log\:3}$

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