Answers.

x=1

Step-by-step explanation:

log2( x^2 -x+2) = 1+2log2(x)

Rewriting 1 as log2(2)

log2( x^2 -x+2) = log2(2)+2log2(x)

We know that a log b = log a^b

log2( x^2 -x+2) = log2(2)+log2(x^2)

we know log a + log b = log (ab)

log2( x^2 -x+2) = log2(2*x^2)

Since the bases are the same the terms inside must be equal

x^2 -x+2 = 2x^2

Subtract 2x^2 from each side

-x^2 -x+2 = 0

Multiply by -1

x^2 +x-2 = 0

Factor

(x+2)(x-1)=0

Using the zero product property

x+2 = 0  x-1=0

x=-2  x=1

Checking the solutions

log2( x^2 -x+2) = 1+2log2(x)

X cannot be negative because 2 log2(x) cannot be negative

log2( 1^2 -1+2) = 1+2log2(1)

x=1

if x = 1, then the answer is 3.5