Please solve the question (Solutions of all 5 questions are very very urgently needed, please help):

Asked by manasd | 17th Sep, 2015, 11:08: PM

Expert Answer:

log subscript x fraction numerator 4 x plus 5 over denominator 6 minus 5 x end fraction space i s space d e f i n e d space f o r space x greater than 0 comma space fraction numerator 4 x plus 5 over denominator 6 minus 5 x end fraction greater than 0 space a n d space x not equal to 1 rightwards double arrow x greater than 0 comma space fraction numerator 4 open parentheses x plus begin display style 5 over 4 end style close parentheses over denominator negative 5 open parentheses x minus begin display style 6 over 5 end style close parentheses end fraction greater than 0 space a n d space x not equal to 1 rightwards double arrow x greater than 0 comma space fraction numerator open parentheses x plus begin display style 5 over 4 end style close parentheses over denominator open parentheses x minus begin display style 6 over 5 end style close parentheses end fraction less than 0 space a n d space x not equal to 1 rightwards double arrow x greater than 0 comma space x element of open parentheses negative 5 over 4 comma space 6 over 5 close parentheses space a n d space space x not equal to 1 rightwards double arrow x element of open parentheses 0 comma space 6 over 5 close parentheses minus open curly brackets 1 close curly brackets...... left parenthesis 1 right parenthesis  C a s e minus 1 colon space 0 less than x less than 1 l o g subscript x fraction numerator 4 x plus 5 over denominator 6 minus 5 x end fraction less than negative 1 rightwards double arrow fraction numerator 4 x plus 5 over denominator 6 minus 5 x end fraction greater than 1 over x rightwards double arrow fraction numerator 4 x plus 5 over denominator 6 minus 5 x end fraction minus 1 over x greater than 0 rightwards double arrow fraction numerator 4 x squared plus 5 x minus 6 plus 5 x over denominator negative 5 x open parentheses x minus begin display style 6 over 5 end style close parentheses end fraction greater than 0 rightwards double arrow fraction numerator 4 x squared plus 10 x minus 6 over denominator x open parentheses x minus 6 over 5 close parentheses end fraction less than 0 rightwards double arrow fraction numerator 2 x squared plus 5 x minus 3 over denominator x open parentheses x minus 6 over 5 close parentheses end fraction less than 0 rightwards double arrow fraction numerator open parentheses x plus 3 close parentheses open parentheses 2 x minus 1 close parentheses over denominator x open parentheses x minus 6 over 5 close parentheses end fraction less than 0 rightwards double arrow fraction numerator open parentheses x plus 3 close parentheses open parentheses x minus begin display style 1 half end style close parentheses over denominator x open parentheses x minus 6 over 5 close parentheses end fraction less than 0 rightwards double arrow x element of open parentheses negative 3 comma space 0 close parentheses space large union space open parentheses 1 half comma space 6 over 5 close parentheses T h e space o n l y space v a l u e s space o f space apostrophe x apostrophe space i n space t h e space a b o v e space i n t e r v a l space s a t i s f y i n g space 0 less than x less than 1 space a r e space x element of open parentheses 1 half comma space 1 close parentheses.... left parenthesis 2 right parenthesis  C a s e space 2 colon space 1 less than x less than 6 over 5 l o g subscript x fraction numerator 4 x plus 5 over denominator 6 minus 5 x end fraction less than negative 1 rightwards double arrow fraction numerator 4 x plus 5 over denominator 6 minus 5 x end fraction less than 1 over x rightwards double arrow fraction numerator 4 x plus 5 over denominator 6 minus 5 x end fraction minus 1 over x less than 0 rightwards double arrow fraction numerator 4 x squared plus 5 x minus 6 plus 5 x over denominator negative 5 x open parentheses x minus begin display style 6 over 5 end style close parentheses end fraction less than 0 rightwards double arrow fraction numerator 4 x squared plus 10 x minus 6 over denominator x open parentheses x minus 6 over 5 close parentheses end fraction greater than 0 rightwards double arrow fraction numerator 2 x squared plus 5 x minus 3 over denominator x open parentheses x minus 6 over 5 close parentheses end fraction greater than 0 rightwards double arrow fraction numerator open parentheses x plus 3 close parentheses open parentheses 2 x minus 1 close parentheses over denominator x open parentheses x minus 6 over 5 close parentheses end fraction greater than 0 rightwards double arrow fraction numerator open parentheses x plus 3 close parentheses open parentheses x minus begin display style 1 half end style close parentheses over denominator x open parentheses x minus 6 over 5 close parentheses end fraction greater than 0 rightwards double arrow x element of open parentheses negative infinity comma space minus 3 close parentheses space large union space open parentheses 0 comma space 1 half close parentheses large union open parentheses 6 over 5 comma space infinity close parentheses N o space v a l u e space i n space t h e space a b o v e space i n t e r v a l space s a t i s f i e s space 1 less than x less than 6 over 5 H e n c e comma space c a s e space 2 space d o e s space n o t space g i v e space a n y space v a l u e space o f space apostrophe x apostrophe. H e n c e comma space t h e space o n l y space v a l u e s space o f space apostrophe x apostrophe space s a t i s f y i n g space t h e space i n e q u a l i t y space a r e space x element of open parentheses 1 half comma space 1 close parentheses space left parenthesis f r o m space left parenthesis 2 right parenthesis right parenthesis

Answered by satyajit samal | 18th Sep, 2015, 02:22: PM