Basic Maths and Logarithm
Logarithmic Equations
Premium Question
Grade 11
Question:
If $\log_2 x + \log_4 x + \log_{16} x = \frac{21}{4}$, then $x$ equals:
(1) $4$
(2) $8$
(3) $16$
(4) $32$
Step-by-Step Solution
Key Concept: $\log_2 x(1 + \frac{1}{2} + \frac{1}{4}) = \frac{21}{4} \Rightarrow \frac{7}{4} \log_2 x = \frac{21}{4} \Rightarrow \log_2 x = 3 \Rightarrow x = 8$.
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Correct Answer: (2)