If 2 to the power of 3 n end exponent over 8 plus 1 plus 3 cross times 2 to the power of n over 2 plus 3 cross times 2 to the power of 2 n end exponent over 4 equals 4913
, then find the value of n.

A) 3

B)10

C) 5

D) 8

 

Asked by adalroshan2464 | 14th Nov, 2018, 05:59: PM

Expert Answer:

begin mathsize 16px style 2 to the power of 3 straight n end exponent over 8 plus 1 plus 3 cross times 2 to the power of straight n over 2 plus 3 cross times 2 to the power of 2 straight n end exponent over 4 equals 4913
open parentheses fraction numerator begin display style 2 to the power of straight n end style over denominator begin display style 2 end style end fraction close parentheses cubed plus 1 plus 3 cross times fraction numerator begin display style 2 to the power of straight n end style over denominator begin display style 2 end style end fraction plus 3 cross times open parentheses fraction numerator begin display style 2 to the power of straight n end style over denominator begin display style 2 end style end fraction close parentheses squared equals 4913
Put space fraction numerator begin display style 2 to the power of straight n end style over denominator begin display style 2 end style end fraction equals straight m
straight m cubed plus 1 plus 3 straight m plus 3 straight m squared equals 4913
straight m cubed plus 3 straight m squared plus 3 straight m plus 1 minus 4913 equals 0
straight m cubed plus 3 straight m squared plus 3 straight m minus 4912 equals 0
left parenthesis straight m minus 16 right parenthesis left parenthesis straight m squared plus 19 straight m plus 307 right parenthesis equals 0
straight m equals 16
fraction numerator begin display style 2 to the power of straight n end style over denominator begin display style 2 end style end fraction equals 16
2 to the power of straight n minus 1 end exponent equals 2 to the power of 4
straight n minus 1 equals 4
straight n equals 5 end style

Answered by Sneha shidid | 15th Nov, 2018, 12:03: PM