Number of solution of {log ₂}(x + 5) = 6 - x is

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Basic of Logarithms

easy

The number of solution of ${\log _2}(x + 5) = 6 - x$ is

A

$2$

B

$0$

C

$3$

D

None of these

Solution

(d) ${\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 $= 1.$

Standard 11

Mathematics

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