ABC26GN2055 · Logarithms

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

If $\log _{4} x+\log _{2} x=6$, then $x$ is equal to
(a)2
(b)4
(c)8
(d)16
Answer
Answer (as printed): D
Explanation
$\log _{4} x+\log _{2} x=6 \Leftrightarrow \frac{\log x}{\log 4}+\frac{\log x}{\log 2}=6 \Leftrightarrow \frac{\log x}{2 \log 2}+\frac{\log x}{\log 2}=6$ $$\begin{aligned} & \Leftrightarrow 3 \log x=12 \log 2 \Leftrightarrow \log x=4 \log 2 \\ & \Leftrightarrow \log x=\log \left(2^{4}\right)=\log 16 \Leftrightarrow x=16 . \end{aligned}$$

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

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