If 3x+1 = 9x-3, Find the Value of 21+X.

If 3^{x + 1} = 9^{x - 3}, find the value of 2^{1 + x}.

Sum

3^{x + 1} = 9^{x - 3}⇒ 3^xx 3 = ( 3² )^{x - 3}
⇒ 3^xx 3 = `3^(2x)/3^6`

⇒ `3^6 xx 3 = 3^(2x)/3^x `

⇒ `3^7 = 3^x`
⇒ x = 7
⇒ `2^( 1 + x ) = 2^( 1 + 7 ) = 2^8 = 256`

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Solving Exponential Equations

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Chapter 7: Indices [Exponents] - Exercise 7 (C) [Page 101]

Chapter 7 Indices [Exponents]
Exercise 7 (C) | Q 5 | Page 101

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