Answer:
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
