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[tex]\frac{ {9}^{x + 1} - {3}^{2x} }{4 \times {3}^{2x - 1} } \\ [/tex]

ans : 6


Sagot :

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{9 {}^{(x + 1)} - 3 {}^{2x} }{4 \times 3 {}^{(2x - 1)} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{3{}^{2(x + 1)} - 3 {}^{2x} }{4 \times 3 {}^{(2x - 1)} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{3{}^{(2x + 2)} - 3 {}^{2x} }{4 \times 3 {}^{(2x - 1)} } [/tex]

here :

  • [tex]{ \sf {3}^{(2x+2)}=({3}^{2x - 1})\sdot (3³)} [/tex]

  • [tex]{ \sf {3}^{(2x)}=({3}^{(2x - 1)})\sdot (3¹)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{3{}^{(2x - 1)}(3 {}^{3} - 3 {}^{1}) }{4 \times 3 {}^{(2x - 1)} } [/tex]

[ taking [tex]{ \sf {3}^{(2x - 1)} } [/tex]common here ]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{27 {}^{} - 3 {}^{}}{4 } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{24{}^{} {}^{}}{4 } [/tex]

[tex]\qquad \sf  \dashrightarrow \: 6[/tex]

Answer is 6 ................

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