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  4. Sum of all the roots of the equation log 7(2x-1)+ log 7(2x-7)=1, is

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Q. Sum of all the roots of the equation $\log _7\left(2^x-1\right)+\log _7\left(2^x-7\right)=1$, is

Continuity and Differentiability

Solution:

$\left(2^x-1\right)\left(2^x-7\right)=7 \Rightarrow x=3$ is the only solution.