ABC26GN2086 · Logarithms
Subject: General Aptitude · Chapter: Logarithms · Exam: · Marks: · Difficulty:
If $\log 3=0.477$ and $(1000)^{x}=3$, then $x$ equals
(a)0.0159
(b)0.0477
(c)0.159
(d)10
Answer
Explanation
$$\begin{aligned} (1000)^{x}=3 & \Rightarrow \log \left[(1000)^{x}\right]=\log 3 \Rightarrow x \log 1000=\log 3 \\ & \Rightarrow x \log \left(10^{3}\right)=\log 3 \Rightarrow 3 x \log 10=\log 3 \\ & \Rightarrow 3 x=\log 3 \\ & \Rightarrow x=\frac{0.477}{3}=0.159 \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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