Find all the real number roots of each equation. Give theexact expression for th

Question

Find all the real number roots of each equation. Give theexact expression for the root, calculator approximation rounded to three decimal places. a)log2(2x2+4)=5 b)log2(x+4)=2-log2(x+1) Find all the real number roots of each equation. Give theexact expression for the root, calculator approximation rounded to three decimal places. a)log2(2x2+4)=5 b)log2(x+4)=2-log2(x+1)

Explanation / Answer

a)log2(2x2+4)=5 --> 2x2+4=25=32 --> 2x2=32-4=28 --> x2=28/2=14 --> x=14 = 3.742 (b) log2(x+4)=2-log2(x+1) --> log2(x+4)+log2(x+1) =2 --> log2[(x+4)*(x+1)]=2 --> (x+4)(x+1)=22=4 --> x2+5x+4=4 --> x2+5x=0 --> x(x+5)=0 --> x= 0 or -5

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