If (5)^{x^{2}+2 x+7}=(125)^{2 x+1} then the value of x is

None of the above/More than one of the above

BPSC 65th Prelims Exam 15 Oct 2019 Solved Paper

Question : 25 of 150

Marks: +1, -0

(5)^{x^{2}+2 x+7}=(125)^{2 x+1}

then the value of

x

Solution:

From the question

(5)^{x^{2}+2 x+7}=(125)^{2 x+1}

⇒(5)^{x^{2}+2 x+7}=\{(5)^{3}\}^{2 x+1}=(5)^{3(2 x+1)}

\;\; =(5)^{6 x+3}

⇒(5)^{x^{2}+2 x+7}=(5)^{6 x+3}

∴ x^{2}+2 x+7=6 x+3

⇒ x^{2}-4 x+4=0

⇒(x-2)^{2}=0 ⇒ x-2=0

⇒ x=2

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