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.
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