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Solve the logarithmic equation: \(log_2 (6 - x) = 3 - log_2 ...

Solve the logarithmic equation: log2(6x)=3log2x

A.

x = 4 or 2

B.

x = -4 or -2

C.

x = -4 or 2

D.

x = 4 or -2

Correct answer is A

log2(6x)=3log2x

log2(6x)=3log22log2x (since log2 2 = 1)

log2(6x)=log223log2x (alog c = log ca)

log2(6x)=log28log2x

log2(6x)=log28x (log a - log b = logab)

6x=8x

x(6x)=8

6xx2=8

x26x+8=0

x24x2x+8=0

x(x4)2(x4)=0

(x4)(x2)=0

x4=0orx2=0

∴ x = 4 or 2