The number of real solution(s) of the equation ${log}_{a} x = | x |, 0 < a < 1,$ is

0

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2

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1

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infinite

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Solution

The correct option is C $1$
The number of real solutions of the equation ${log}_{a} x = | x |$ is equal to the number of point of intersection of the curves $y = | x |$ and $y = {log}_{a} x,$ shown as

It is evident from the graph that these curves intersects at one points only.
$∴$ There is only $1$ solution.

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