ABC26GN2009 · Logarithms
Subject: General Aptitude · Chapter: Logarithms · Exam: 2006 · Marks: · Difficulty:
If $\log _{10}\left(x^{2}-6 x+45\right)=2$, find the value of $x$. (R.R.B., 2006)
Answer
Explanation
$\log _{10}\left(x^{2}-6 x+45\right)=2 \Rightarrow x^{2}-6 x+45=10^{2}=100$ $$\begin{aligned} & \Rightarrow x^{2}-6 x-55=0 \Rightarrow x^{2}-11 x+5 x-55=0 \\ & \Rightarrow x(x-11)+5(x-11)=0 \Rightarrow(x-11)(x+5)=0 \\ & \Rightarrow x=11 \text { or } x=-5 \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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