If 3^x + 27(3^{–x}) = 12, then what is the value of x?

RRB NTPC Mains or Stage 2 Model Paper 6 with solutions

Question : 16 of 119

Marks: +1, -0

3^x + 27(3^{–x}) = 12

, then what is the value of x?

Solution:

^+ 27(3^{–x}) = 12Let 3^x = y

∴Y+27/y= 12

⇒y^2 – 12y + 27 = 0

⇒y^2 – 9y – 3y + 27 = 0

⇒ (y – 3)(y – 9) = 0 Þ y = 3, 9

when y = 3; when y = 9

⇒ 3^x = 3

3^x = 9

∴x = 1 x = 2
x = 1, 2 are value of x

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