If log10 (x2 – 3x + 6) = 1, then the value of x is A) 4 or -1 B) 4

1.	If log10 (x2 – 3x + 6) = 1, then the value of x is A) 4 or -1 B) 4 only C) 10 or 2 D) 4 or -2
Answer» Correct option is (A) 4 or -1 Given equation is \(log_{10}(x^2-3x+6)=1\) \(\Rightarrow x^2-3x+6=10^1=10\) (By taking anti-log) \(\Rightarrow x^2-3x+6-10=0\) \(\Rightarrow x^2-4x+x-4=0\) \(\Rightarrow x(x-4)+1(x-4)=0\) \(\Rightarrow(x-4)(x+1)=0\) \(\Rightarrow x+1=0\) \(or\;x-4=0\) \(\Rightarrow\) x = -1 or x = 4 Correct option is A) 4 or -1

If log10 (x2 – 3x + 6) = 1, then the value of x is A) 4 or -1 B) 4 only C) 10 or 2 D) 4 or -2

Answer»

Correct option is (A) 4 or -1

Given equation is

\(log_{10}(x^2-3x+6)=1\)

\(\Rightarrow x^2-3x+6=10^1=10\) (By taking anti-log)

\(\Rightarrow x^2-3x+6-10=0\)

\(\Rightarrow x^2-4x+x-4=0\)

\(\Rightarrow x(x-4)+1(x-4)=0\)

\(\Rightarrow(x-4)(x+1)=0\)

\(\Rightarrow x+1=0\) \(or\;x-4=0\)

\(\Rightarrow\) x = -1 or x = 4

Correct option is A) 4 or -1