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Sir pls solve the following.
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Asked by rsudipto | 27 Dec, 2018, 21:53: PM
answered-by-expert Expert Answer
Raised to the power of a base number and logarithm to the same base are reciprocal to each other.
 
Hence the given expression is written as,  begin mathsize 12px style open curly brackets space open parentheses square root of 9 to the power of x minus 1 end exponent plus 7 end root space close parentheses space plus space open parentheses 3 to the power of x minus 1 end exponent plus 1 close parentheses to the power of bevelled fraction numerator negative 1 over denominator 5 end fraction end exponent space close curly brackets to the power of 7 end style
6th term of binomial expansion is given by,
 
  begin mathsize 12px style C presuperscript 7 subscript 5 space open parentheses square root of 9 to the power of x minus 1 end exponent plus 7 end root close parentheses squared space space open square brackets open parentheses 3 to the power of x minus 1 end exponent plus 1 close parentheses to the power of bevelled fraction numerator negative 1 over denominator 5 end fraction end exponent close square brackets to the power of 5 space space space equals space C presuperscript 7 subscript 5 open parentheses 9 to the power of x minus 1 end exponent plus 7 close parentheses space open parentheses 3 to the power of x minus 1 end exponent plus 1 close parentheses to the power of negative 1 end exponent space equals space 84 H e n c e comma space space space 21 space open parentheses fraction numerator 9 to the power of x minus 1 end exponent plus 7 over denominator 3 to the power of x minus 1 end exponent plus 1 end fraction close parentheses space space equals space 84 space space space space space o r space space space fraction numerator 9 to the power of x minus 1 end exponent plus 7 over denominator 3 to the power of x minus 1 end exponent plus 1 end fraction space equals space 4 H e n c e comma space space 9 to the power of x minus 1 end exponent plus 7 space equals space 4 space open parentheses 3 to the power of x minus 1 end exponent plus 1 close parentheses 9 to the power of x over 9 space plus space 7 space equals space fraction numerator 4 cross times 3 to the power of x over denominator 3 end fraction space plus space 4 9 to the power of x space plus space 63 space equals space 12 cross times 3 to the power of x space plus space 36 3 to the power of 2 x end exponent space minus space 12 cross times 3 to the power of x space plus space 27 space equals space 0 L e t space u s space s u b s t i t u t e comma space space space y space equals space 3 to the power of x space comma space t h e n space w e space h a v e space space y squared space minus space 12 y space plus space 27 space equals space left parenthesis y minus 3 right parenthesis left parenthesis y minus 9 right parenthesis space equals 0 i f space y space equals space 3 comma space t h e n space 3 to the power of x space equals space 3 space comma space space h e n c e space x space equals 1 i f space y space equals space 9 comma space t h e n space 3 to the power of x space equals space 9 comma space space h e n c e space x space equals 2 end style
Answered by Thiyagarajan K | 28 Dec, 2018, 00:25: AM

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