If 27^{x}+27^{[x-(1 / 3)]}=972, then what is the value of x ?

SSC CGL 16 Aug 2017 Shift 1 Paper

Question : 64 of 100

Marks: +1, -0

27^{x}+27^{[x-(1 / 3)]}=972,

then what is the value of

x ?

Solution:

27^{x}+27^{ x-(1 / 3) }=972

⇒

27^{x} [1+(27)^{- {1}/{3}} ]=972

⇒

27^{x} [1+ {1}/{3} ]=972

⇒

27^{x} [4/3 ]=972

⇒

27^{x}×{1}/{3}= {972}/{4}

⇒ 3^{3 x} . 3^{-1}=243⇒ 3^{3 x-1}=(3)^{5}

On comparing,

⇒ 3 x-1=5 ⇒3 x=6

∴ x=2

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