1/( Log_A Bc + 1) + 1/(Log_B Ca + 1) + 1/ ( Log_C Ab + 1 ) – Mathematics | Shaalaa.com

Sum

Evaluate :`1/( log_a bc + 1) + 1/(log_b ca + 1) + 1/ ( log_c ab + 1 )`

Solution

⇒ `1/( log_a bc + 1) + 1/(log_b ca + 1) + 1/ ( log_c ab + 1 )`

⇒`1/( log_a bc + log_a a) + 1/(log_b ca +log_b b) + 1/ ( log_c ab + log_c c )`

⇒ `1/( log_a abc ) + 1/(log_b abc) + 1/ ( log_c abc )`  …[∵ loga b + loga c = loga bc ]

⇒ `(1) /[( log abc ) / ( loga )]` + `(1) /[( log abc ) / ( logb )]` + `(1) /[( log abc ) / ( logc )]`

⇒ ` ( log a + log b + log c) / ( log abc) `

⇒ `( log abc) / ( log abc) `  …∵[ loga b + loga c = loga bc ] 

⇒ 1

Concept: More About Logarithm

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Selina Concise Mathematics Class 9 ICSE