x = 4 or 2
x = -4 or -2
x = -4 or 2
x = 4 or -2
Correct answer is A
log2(6−x)=3−log2x
⇒ log2(6−x)=3log22−log2x (since log2 2 = 1)
⇒ log2(6−x)=log223−log2x (alog c = log ca)
⇒ log2(6−x)=log28−log2x
⇒log2(6−x)=log28x (log a - log b = logab)
⇒ 6−x=8x
⇒ x(6−x)=8
⇒ 6x−x2=8
⇒ x2−6x+8=0
⇒ x2−4x−2x+8=0
⇒ x(x−4)−2(x−4)=0
⇒ (x−4)(x−2)=0
⇒ x−4=0orx−2=0
∴ x = 4 or 2
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