Math, asked by sudhashaw9804, 8 months ago

3^(x^2) :3^x=9:1, find x​

Answers

Answered by mysticd
0

 Given \: 3^{(x^{2})} : 3^{x} = 9 : 1

 \implies 3^{(x^{2})} \times 1 =  3^{x} \times 9

 \blue{ ( Product \: of \: extrems = Product \: of \: means ) }

 \implies 3^{(x^{2})} = 3^{x} \times 3^{2}

 \implies 3^{(x^{2})} = 3^{x+2}

/* By Exponential Law */

 \boxed{ \pink{ x^{m} \times x^{n} = x^{m+n} }}

 \implies x^{2} = x + 2

 \implies x^{2} -x - 2 = 0

 \implies x^{2} -2x+1x - 2 = 0

 \implies x(x-2) +1(x-2) = 0

 \implies (x-2)(x+1) = 0

 \implies x-2 = 0 \: Or \: x+1 = 0

 \implies x = 2 \: Or \: x = -1

Therefore.,

\green { x = 2 \: Or \: x = -1}

•••♪

Answered by Anonymous
1

{\tt{\purple{\underline{\underline{\huge{Answer:}}}}}}

{\pink{\boxed{Given}}}

\sf\implies \: 3^{(x^{2})} : 3^{x} = 9 : 1

 \implies 3^{(x^{2})} \times 1 =  3^{x} \times 9

  ( Product \: of \: extrems = Product \: of \: means

 \implies 3^{(x^{2})} = 3^{x} \times 3^{2}

 \implies 3^{(x^{2})} = 3^{x+2}

 \boxed{ x^{m} \times x^{n} = x^{m+n} }

 \implies x^{2} = x + 2

 \implies x^{2} -x - 2 = 0

 \implies x^{2} -2x+1x - 2 = 0

 \implies x(x-2) +1(x-2) = 0

 \implies (x-2)(x+1) = 0

 \implies x-2 = 0 \: Or \: x+1 = 0

 \implies x = 2 \: Or \: x = -1

__________________________

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