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The identity \( \Large log_{a}n\ log_{b}n\ +\ log_{b}n\ log_{c}n\ +\ log_{c}n\ log_{a}n \) ls:

A) \( \Large \frac{log_{a}n\ log_{b}n\ log_{c}n}{log_{abc}n} \)
B) \( \Large \frac{log_{abc}n}{log_{a}n} \)
C) \( \Large \frac{log_{b}n}{log_{abc}n} \)
D) none of these

Correct Answer:

A) \( \Large \frac{log_{a}n\ log_{b}n\ log_{c}n}{log_{abc}n} \)

Description for Correct answer:

\( \Large log_{a}n \ log_{b}n+log_{b}n \ log_{c}n+log_{c}n \ log_{a}n \)

=\( \Large \frac{1}{log_{n}a \ log_{n}b}+\frac{1}{log_{n}b \ log_{n}c}+\frac{1}{log_{n}c \ log_{n}a} \)

\( \Large \left[ \therefore log_{m}n=\frac{1}{log_{n}m} \right] \)

= \( \Large \frac{log_{n}c+log_{n}a+log_{n}b}{log_{n}a \ log_{n}b \ log_{n}c} \)

= \( \Large \frac{log_{n} \left(abc\right) }{log_{n}a \ log_{n}b \ log_{n}c}=\frac{log_{a}n \ log_{b}n \ log_{c}n}{log_{abc}n} \)

Part of solved Logarithms questions and answers : >> Elementary Mathematics >> Logarithms

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