The number of solutions of ${log}_{2} (x + 5) = 6 - x$ is

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Solution

We have
${log}_{2} (x + 5) = 6 - x \Rightarrow x + 5 = 2^{6 - x}$
In order to find the values of $x$ satisfying the above equations, let us consider the graphs of the functions $y = x + 5$ and $y = 2^{6 - x}$ .
We observe that the two curves intersect at exactly one point. Hence, the given equation has exactly one solution.

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