QJEEM21Ma5fbd: JEE Main 2021 Mathematics - Class 12 JEEM21Ma5fbd Solution: The number of solutions of the equation log 4 (x 1) = log 2 (x…

${\log _4}(x - 1) = {\log _2}(x - 3)$

$\Rightarrow {1 \over 2}{\log _2}(x - 1) = {\log _2}(x - 3)$

$\Rightarrow {\log _2}{(x - 1)^{1/2}} = {\log _2}(x - 3)$

$\Rightarrow {(x - 1)^{1/2}} = {\log _2}(x - 3)$

$\Rightarrow {(x - 1)^{1/2}} = x - 3$

$\Rightarrow x - 1 = {x^2} + 9 - 6x$

$\Rightarrow {x^2} - 7x + 10 = 0$

$\Rightarrow (x - 2)(x - 5) = 0$

$\Rightarrow x = 2,5$

But x $\ne$ 2 because it is not satisfying the domain of given equation i.e. log₂(x $-$ 3) $\to$ its domain x > 3

finally x is 5

$\therefore$ No. of solutions = 1.