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Q. The value of $49^{ A }+5^{ B }$, where $A =1-\log _7 2$ and $B =-\log _5 4$ is

Continuity and Differentiability

Solution:

$ 49^{1-\log _7 2}+5^{-\log _5 4} $
$=49^{\log _7 7-\log _7 2}+\frac{1}{5^{\log _5 4}} $
$=49^{\log _7\left(\frac{7}{2}\right)}+\frac{1}{4} $
$=\frac{49}{4}+\frac{1}{4}=\frac{50}{4}=\frac{25}{2}=12.5$