Value of x in expression {[x + {x^{{{log }_{10}}}}^{(x)}]^5} , if third term in expansion is 10,00,0

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7.Binomial Theorem

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The value of $x$ in the expression ${[x + {x^{{{\log }_{10}}}}^{(x)}]^5}$, if the third term in the expansion is $10,00,000$

A

$10$

B

$11$

C

$12$

D

None of these

Solution

(a) ${T_3} = {\,^5}{C_2}.{x^2}{({x^{{{\log }_{10}}x}})^3} = {10^6}$

Put . $^5{C_2} = 10\,\,\,\,\,[{\log _{10}}10 = 1]$

If $x = 10$, then ${10^3}{.10^{2.1}} = {10^5}$ is satisfied.

Hence $ x =10.$

Standard 11

Mathematics

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