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  4. Let x is the value of satisfying the equation 5 log 10 x=50-x log 10 5. Then find the value of (x/50).

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Q. Let $x$ is the value of satisfying the equation $5^{\log _{10} x}=50-x^{\log _{10} 5}$. Then find the value of $\frac{x}{50}$.

Continuity and Differentiability

Solution:

Put $5^{\log _{10} x}= t $
$2 t =50 \Rightarrow t =25$
$\Rightarrow 5^{\log _{10} x}=5^2 \Rightarrow x=100 \Rightarrow \frac{x}{50}=2$