Question

16. Solve for x in each of the following (hint: logs or factoring): A. 32-x-4 = 16-2x+1 B. x4 +7x3 +12x2 = 0

Answer 1

Case: Exponential equations

Method:

a)

`\begin{gathered} 32^(-x-4)=16^(-2x+1) \\ 2^(5(-x-4))=2^(4(-2x+1)) \\ 5(-x-4)=4(-2x+1) \\ -5x-20=-8x+4 \\ -5x+8x=4+20 \\ 3x=24 \\ x=(24)/(3) \\ x=8 \end{gathered}`

b)

`\begin{gathered} x^4+7x^3+12x^2=0 \\ Factorizing \\ x^2(x^2+7x+12)=0 \\ x^2(x^2+4x+3x+12)=0 \\ x^2[x(x+4)+3(x+4)]=0 \\ x^2(x+4)(x+3)=0 \\ x=0,\text{ }x=-4\text{ OR }x=-3 \end{gathered}`

Final answer:

a) x= 8

b) x= 0 or -4 or -3