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The-roots-of-the-equation-2-x-2-3-3x-x-1-9-are-given-by-

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Question Number 48735 by Pk1167156@gmail.com last updated on 28/Nov/18
The roots of the equation 2^(x+2) ∙ 3^((3x)/(x−1)) = 9 are given by
Therootsoftheequation2x+2⋅33xx−1=9aregivenby
Answered by Smail last updated on 28/Nov/18
2^(x+2) .3^((3x)/(x−1)) =9= (x+2)ln(2)+((3x)/(x−1))ln3=2ln3 (x^2 +x−2)ln2+3xln3−2xln3+2ln3=0 x^2 ln2+(ln2+ln3)x+2(ln3−ln2)=0 x^2 +((ln2+ln3)/(ln2))x+((2(ln3−ln2))/(ln2))=0 x(x+2)+((ln3−ln2)/(ln2))(x+2)=0 (x+2)(x+((ln3−ln2)/(ln2)))=0 x=−2 or x=1−((ln3)/(ln2))
2x+2.33xx−1=9=(x+2)ln(2)+3xx−1ln3=2ln3(x2+x−2)ln2+3xln3−2xln3+2ln3=0x2ln2+(ln2+ln3)x+2(ln3−ln2)=0x2+ln2+ln3ln2x+2(ln3−ln2)ln2=0x(x+2)+ln3−ln2ln2(x+2)=0(x+2)(x+ln3−ln2ln2)=0x=−2orx=1−ln3ln2

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