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  • The value of x in the expression <img alt="\left[x+x^{\log _{10}(x)}\right]^5" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cleft%5Bx&plus;x%5E%7B%5Clog%20_%7B10%7D%28x%29%7D%5Cright%

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

Option: 1

10


Option: 2

11


Option: 3

12


Option: 4

None of these


Answers (1)

best_answer

\begin{aligned} & T_3={ }^5 C_2 \cdot x^2\left(x^{\log _{10} x}\right)^3=10^6 \\ \end{aligned}

Put \begin{aligned} { }^5 C_2=10 \quad\left[\log _{10} 10=1\right] \end{aligned}

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

Hence x =10.

Posted by

Gautam harsolia

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