ABC26GN2010 · Logarithms
Subject: General Aptitude · Chapter: Logarithms · Exam: 2002 · Marks: · Difficulty:
Find the value of $x$ which satisfies the relation $\log _{10} 3+\log _{10}(4 x+1)=\log _{10}(x+1)+1$ (M.B.A., 2002)
Answer
Explanation
$$\begin{aligned} & \log _{10} 3+\log _{10}(4 x+1)=\log _{10}(x+1)+1 \\ \Leftrightarrow & \log _{10} 3+\log _{10}(4 x+1)=\log _{10}(x+1)+\log _{10} 10 \\ \Leftrightarrow & \log _{10}[3(4 x+1)]=\log _{10}[10(x+1)] \\ \Leftrightarrow & 3(4 x+1)=10(x+1) \Leftrightarrow 12 x+3=10 x+10 \Leftrightarrow 2 x=7 \Leftrightarrow x=\frac{7}{2} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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