Question

1/log 210 to the base 5+ 1/log 210 to the base 6 + 1/log 210 to base 7​

Answer 1

Hey Buddy

Here's The Answer

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Properties Used :

=> logₐ ( b ) = log b/log a ______ ( i )

=> log a + log b = log ( ab ) _______ ( ii )

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Q : ( 1 / log₅ 210 ) + ( 1 / log₆ 210 ) + ( 1 / log₇ 210 )

Using property ( i )

=> ( 1 / log 210/log 5 ) + ( 1 / log 210/log 6 ) + ( 1 / log 210/log 7 )

=> log 5/log 210 + log 6/log 210 + log 7/log 210

Taking log 210 as LCM

=> ( log 5 + log 6 + log 7 )/ log 210

Using property ( ii )

=> log ( 5 × 6 × 7 )/log 210

=> log ( 210 )/ log 210

=> 1

Hope It Helps ^^