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  4. If λ= log 0.001 10000, then anti log 103(λ) is equal to

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Q. If $\lambda=\log _{0.001} 10000$, then anti $\log _{10^3}(\lambda)$ is equal to

Continuity and Differentiability

Solution:

$ \lambda=\log _{10^{-3}}\left(10^4\right)=\frac{-4}{3} $
$\therefore \text { anti } \log _{10^3}\left(\frac{-4}{3}\right)=\left(10^3\right)^{\frac{-4}{3}}=10^{-4}=0.0001$