WBJEE · Maths · Sequences and Series
Let \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) be real numbers, each greater than 1 , such that \(\frac{2}{3} \log _{\mathrm{b}} \mathrm{a}+\frac{3}{5} \log _{\mathrm{c}} \mathrm{b}+\frac{5}{2} \log _{\mathrm{a}} \mathrm{c}=3\). If the value of \(b\) is 9 , then the value of ' \(a\) ' must be
- A \(\sqrt[3]{81}\)
- B \(\frac{27}{2}\)
- C 18
- D 27
Answer & Solution
Correct Answer
(D) 27
Step-by-step Solution
Detailed explanation
\(\frac{2 \ln a}{3 \ln b}+\frac{3 \ln b}{5 \ln c}+\frac{5 \ln c}{2 \ln a}=3\) By A.M \(=\) G.M \(\frac{2 \ln a}{3 \ln b}=1\) \(\Rightarrow a^{2}=b^{3} \Rightarrow a=\left(3^{6}\right)^{1 / 2}=3^{3} \Rightarrow a=27\)
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