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ICSE Class 9 Answered

Please solve these questions.
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Asked by Kanwaranita10 | 06 Feb, 2019, 03:27: PM
answered-by-expert Expert Answer
begin mathsize 16px style log subscript x 2 space cross times space log subscript x over 16 end subscript 2 space equals space log subscript x over 64 end subscript 2 fraction numerator 1 over denominator open parentheses log subscript 2 x close parentheses space open parentheses log subscript 2 begin display style x over 16 end style close parentheses end fraction space equals space fraction numerator 1 over denominator log subscript 2 begin display style x over 64 end style end fraction fraction numerator 1 over denominator open parentheses log subscript 2 x close parentheses open square brackets log subscript 2 x space minus space log subscript 2 16 close square brackets end fraction space equals space fraction numerator 1 over denominator log subscript 2 x space minus space log subscript 2 64 end fraction B y space e q u a t i n g space d e n o m i n a t o r s open parentheses log subscript 2 x close parentheses open square brackets log subscript 2 x space minus space 4 close square brackets space equals space log subscript 2 x space minus space 6 space space space space.............. left parenthesis 1 right parenthesis l e t space alpha space equals space log subscript 2 x T h e n space e q n. left parenthesis 1 right parenthesis space c a n space b e space w r i t t e n space a s comma space space alpha open parentheses alpha minus 4 close parentheses space equals space alpha space minus space 6 alpha squared space minus 5 alpha space plus space 6 space equals space 0 open parentheses alpha minus 2 close parentheses open parentheses alpha minus 3 close parentheses space equals space 0 h e n c e space alpha space equals space 2 space space o r space space alpha space equals space 3 i f space alpha space equals space 2 comma space space log subscript 2 x space equals space 2 space space space space o r space x space equals space 2 squared space equals space 4 i f space alpha space equals space 3 comma space space log subscript 2 x space equals space 3 space space space space o r space x space equals space 2 cubed space equals space 8 end style
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begin mathsize 16px style log subscript 5 open parentheses 5 to the power of 1 over x end exponent space plus space 125 close parentheses space equals space log subscript 5 6 space plus space 1 space plus space fraction numerator 1 over denominator 2 x end fraction space equals space log subscript 5 6 space plus space log subscript 5 5 plus fraction numerator 1 over denominator 2 x end fraction log subscript 5 5 log subscript 5 open parentheses 5 to the power of 1 over x end exponent space plus space 125 close parentheses space equals log subscript 5 open parentheses 30 cross times 5 to the power of fraction numerator 1 over denominator 2 x end fraction end exponent close parentheses h e n c e comma space space space open parentheses 5 to the power of 1 over x end exponent space plus space 125 close parentheses space equals space open parentheses 30 cross times 5 to the power of fraction numerator 1 over denominator 2 x end fraction end exponent close parentheses space............ left parenthesis 1 right parenthesis l e t space alpha space equals space 5 to the power of fraction numerator 1 over denominator 2 x end fraction end exponent e q n. left parenthesis 1 right parenthesis space b e c o m e s comma space space alpha squared plus 125 space equals 30 alpha space space........... left parenthesis 2 right parenthesis h e n c e space alpha squared space minus space 30 alpha plus 125 space equals space open parentheses alpha minus 25 close parentheses open parentheses alpha minus 5 close parentheses space equals space 0 space............ left parenthesis 3 right parenthesis h e n c e space alpha space equals space 5 space space space o r space alpha space equals space 25 i f space alpha space equals space 5 comma space t h e n space 5 to the power of fraction numerator 1 over denominator 2 x end fraction end exponent space equals space 5 space space space space o r space x space equals space 1 half i f space alpha space equals space 25 comma space t h e n space 5 to the power of fraction numerator 1 over denominator 2 x end fraction end exponent space equals space 5 squared space space space space o r space x space equals space 1 fourth end style
Answered by Thiyagarajan K | 06 Feb, 2019, 06:41: PM

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