Question

The number of solution of $\log_{2} (x + 5) = 6 - x$ is

Easy

Solution

$\log_{2} (x + 5) = 6 - x \Rightarrow x + 5 = 2^{6 - x} \Rightarrow x + 5 = 64 . 2^{- x}$
Let $y = x + 5, y = 64 . 2^{- x}$ will intersect at one point.
Number of solutions = 1.

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