Solve the following equations for x :
(i) 3x+1=27\sqrt{3^{x + 1}} = 273x+1=27
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(i) Solving,
⇒3x+1=27⇒3x+1=33⇒3x+1=36⇒x+1=6⇒x=6−1=5.\Rightarrow \sqrt{3^{x + 1}} = 27 \\[1em] \Rightarrow \sqrt{3^{x + 1}} = 3^3 \\[1em] \Rightarrow \sqrt{3^{x + 1}} = \sqrt{3^6} \\[1em] \Rightarrow x + 1 = 6 \\[1em] \Rightarrow x = 6 - 1 = 5.⇒3x+1=27⇒3x+1=33⇒3x+1=36⇒x+1=6⇒x=6−1=5.
Hence, x = 5.
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