The set of all real numbers x for which                                                              log2004(log2003(log2002(log2001x ))) is defined as {x|x>c} then the value of c is

Asked by Kalyanrao Chavan | 18th Jul, 2014, 10:53: PM

Expert Answer:

G i v e n space t h a t space t h e space e x p r e s s i o n space log subscript 2004 open parentheses log subscript 2003 open parentheses log subscript 2002 open parentheses log subscript 2001 open parentheses x close parentheses close parentheses close parentheses close parentheses space i s space d e f i n e d. L o g a r i t h m space o f space a n y space n u m b e r space i s space v a l i d space o n l y space i f log subscript 2003 open parentheses log subscript 2002 open parentheses log subscript 2001 open parentheses x close parentheses close parentheses close parentheses greater than 0 T a k i n g space 2003 space t o space t h e space p o w e r space o n space b o t h space t h e space s i d e s comma space w e space h a v e 2003 to the power of log subscript 2003 open parentheses log subscript 2002 open parentheses log subscript 2001 open parentheses x close parentheses close parentheses close parentheses end exponent greater than 2003 to the power of 0 rightwards double arrow log subscript 2002 open parentheses log subscript 2001 open parentheses x close parentheses close parentheses greater than 1 space space space space left square bracket sin c e space a to the power of log subscript a b end exponent equals b space a n d space 2003 to the power of 0 equals 1 right square bracket T a k i n g space 2002 space t o space t h e space p o w e r space o n space b o t h space t h e space s i d e s comma space w e space h a v e log subscript 2001 open parentheses x close parentheses greater than 2002 to the power of 1 space space space space space left square bracket sin c e space a to the power of log subscript a b end exponent equals b right square bracket rightwards double arrow log subscript 2001 open parentheses x close parentheses greater than 2002 T a k i n g space 2001 space t o space t h e space p o w e r space o n space b o t h space t h e space s i d e s comma space w e space h a v e x greater than 2001 to the power of 2002 T h u s space t h e space v a l u e space o f space c equals 2001 to the power of 2002

Answered by Vimala Ramamurthy | 20th Jul, 2014, 08:15: AM