9∧(x+2) + 6.3∧(x+1) + 1 = 0
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9^(x + 2) +6.3^(x +1) +1 =0
use concept ,
x^(m+ n) = x^m.x^n here
so,
9^x.9^2 +6.3^x.3^1 + 1=0
81.9^x + 18.3^x +1 =0
81.(3^2)^x + 18.3^x +1 =0
81.3^2x + 18.3^x +1 =0
let 3^x = r
then 3^2x = r²
so ,
81r² +18r +1 =0
(9r)² +2.(9r).1 + 1 =0
(9r +1 )² =0
r = -1/9
but r = 3^x
so, 3^x = -1/9
but we know, exponential term is always positive .
so, here no solution
use concept ,
x^(m+ n) = x^m.x^n here
so,
9^x.9^2 +6.3^x.3^1 + 1=0
81.9^x + 18.3^x +1 =0
81.(3^2)^x + 18.3^x +1 =0
81.3^2x + 18.3^x +1 =0
let 3^x = r
then 3^2x = r²
so ,
81r² +18r +1 =0
(9r)² +2.(9r).1 + 1 =0
(9r +1 )² =0
r = -1/9
but r = 3^x
so, 3^x = -1/9
but we know, exponential term is always positive .
so, here no solution
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