ABC26GN2065 · Logarithms

Subject: General Aptitude · Chapter: Logarithms · Exam: · Marks: · Difficulty:

If $\log _{10} 5+\log _{10}(5 x+1)=\log _{10}(x+5)+1$, then $x$ is equal to
(a)1
(b)3
(c)5
(d)10
Answer
Answer (as printed): B
Explanation
$\log _{10} 5+\log _{10}(5 x+1)=\log _{10}(x+5)+1$ $$\begin{aligned} & \Rightarrow \quad \log _{10} 5+\log _{10}(5 x+1)=\log _{10}(x+5)+\log _{10} 10 \\ & \Rightarrow \quad \log _{10}[5(5 x+1)]=\log _{10}[10(x+5)] \\ & \Rightarrow \quad 5(5 x+1)=10(x+5) \\ & \Rightarrow \quad 5 x+1=2 x+10 \Rightarrow 3 x=9 \Rightarrow x=3 \end{aligned}$$

Explanation as extracted from the printed page; notation may be imperfect.

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