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Q.
The ratio $\frac{2^{\log _{2^{1 / 4}} a }-3^{\log _{27}\left( a ^2+1\right)^3}-2 a }{7^{4 \log _{49} a }- a -1}$ simplifies to
Continuity and Differentiability
Solution:
$\frac{2^{\log _{2^{1 / 4}} a }-3^{\log _{27}\left( a ^2+1\right)^3}-2 a }{7^{4 \log _{49} a }- a -1}=\frac{2^{4 \log _2 a }-3^{3 \log _{3^3}\left( a ^2+1\right)}}{7^{4 \log _{7^2} a }- a -1}=\frac{ a ^4- a ^2-2 a -1}{ a ^2- a -1}\left[ a ^4-( a -1)^2\right] \Rightarrow D$