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  4. If a =1- log 7 2 and b = log 5((1/4)) then the value of (49) a +5 b equals

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Q. If $a =1-\log _7 2$ and $b =\log _5\left(\frac{1}{4}\right)$ then the value of $(49)^{ a }+5^{ b }$ equals

Continuity and Differentiability

Solution:

Given, $a =1-\log _7 2, b =\log _5\left(\frac{1}{4}\right)$
Now, Let $E=49^{ a }+5^{ b }=49^{1-\log _7 2}+5^{\log _5\left(\frac{1}{4}\right)}=49 \cdot 7^{-\log _7 4}+\frac{1}{4}=\frac{49}{4}+\frac{1}{4}=\frac{50}{4}=\frac{25}{2}$