If the value of is then find the value of

JEE MainMathematicsToughLogarithm and its applications

If the value of
$\left( \frac{1}{49} \right)^{1 + \log_{7}2} + 5^{- \log_{1/5}7}$ is
$a + \frac{1}{b}(where\ a,b \in N)$ then find the value of $\frac{b}{a}$

Show answer and solution

\left( \frac{1}{49} \right)^{1 + \log_{7}2} + 5^{\log_{1/5}7}

\left( \frac{1}{49} \right) \times \left( \frac{1}{49} \right)^{\log_{7}2 + 5^{- \log_{(5)^{- 1}}\ 7}}

= \frac{1}{49} \times (7)^{- 2\log_{7}2} + 5^{\log_{5}7}

= \frac{1}{49} \times 7^{\log_{7}(2)^{2}} + 5^{\log_{5}7}

= \frac{1}{49} \times \frac{1}{4} + 7 = \frac{1}{196} + 7 = a + \frac{1}{b}

\Rightarrow a = 7,b = 196

\Rightarrow b/a = 28

Source: Grass-G / M-05 Mathematics Paper 10 October.docx

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