ABC26GN2081 · Logarithms
Subject: General Aptitude · Chapter: Logarithms · Exam: 2010 · Marks: · Difficulty:
If $\log _{3} x+\log _{9} x^{2}+\log _{27} x^{3}=9$, then $x$ equals
(a)3
(b)9
(c)27
(d)None of these
Answer
Explanation
$$\log_{3}x+\log_{9}x^{2}+\log_{27}x^{3}=9 \Rightarrow \log_{3}x+\log_{3^{2}}x^{2}+\log_{3^{3}}x^{3}=9 \Rightarrow \log_{3}x+\frac{2}{2}\log_{3}x+\frac{3}{3}\log_{3}x=9 \Rightarrow 3\log_{3}x=9 \Rightarrow \log_{3}x=3 \Rightarrow x=3^{3}=27$$
Explanation as extracted from the printed page; notation may be imperfect.
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