Question: Solve: 4×3^{x+1} - 9^x = 27


Solution:
Given,

4×3^{x+1} - 9^x = 27

or, 4×3^x×3^1 - 9^x = 27

or, 12×3^x - (3^2)^x = 27

or, 12×3^x - (3^x)^2 = 27

[ Let 3^x = a ]

or, 12a - a^2 = 27

or, a² - 12a +27 = 0

or, a² - (9+3)a + 27 = 0

or, a² -9a -3a +27= 0

or, a(a-9) - 3(a-9) = 0

or, (a-3)(a-9) = 0

Either,

a-3 = 0

or, 3^x = 3^1

\therefore x= 1

Or,

a -9 = 0

or, 3^x = 9

or, 3^x = 3²

\therefore x = 2

Hence, the possible values of x are 1 and 2.

Related Notes and Solutions:

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