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  4. If 13 log 10 x=338-x log 10 13, then the value of (x+2) is equal to

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Q. If $13^{\log _{10} x}=338-x^{\log _{10} 13}$, then the value of $(x+2)$ is equal to

Continuity and Differentiability

Solution:

$ \text { Given, } 13^{\log _{10} x}=338- x ^{\log _{10} 13} \Rightarrow 13^{\log _{10} x}=169=13^2 \quad\left(14^{\log _{10} x}=x^{\log _{10} 13}\right) $
$\therefore \log _{10} x=2$
$\therefore x=100 \Rightarrow(x+2)=102$