Question 23

Let $$a = \dfrac{(\log_7 4)(\log_7 5 - \log_7 2)}{\log_7 25(\log_7 8 - \log_7 4)}$$. Then the value of $$5^a$$ is

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$$a = \dfrac{(\log_7 4)(\log_7 5 - \log_7 2)}{\log_7 25(\log_7 8 - \log_7 4)}$$ 

$$a=\dfrac{\ 2\left(\log_72\right)\left(\log_72.5\right)}{2\left(\log_75\right)\left(\log_72\right)}$$

$$a=\dfrac{\ \log_72.5}{\log_75}=\log_52.5$$

Therefore ,$$5^a=2.5$$

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