The discussion focuses on simplifying the expression (\log_a{b})(\log_b{c})(\log_c{d}) in terms of \log_x{y}. The solution involves converting each logarithm to a common base, specifically base 'a'. The final simplified expression is log_a d, demonstrating that the original expression can be represented as a single logarithm. The misunderstanding regarding the presence of 'x' and 'y' is clarified, emphasizing the requirement to express the result in terms of a single logarithm.
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HallsofIvy said:Since there are no "x" or "y" in the problem I think you are misunderstanding.
"in term so log_x y" simply means "in terms of a single logarithm"
You could, for example, put everything in terms of a logarithm base a:
log_b c= \frac{log_a c}{log_a b}
and
log_c d= \frac{log_a d}{log_a c}
so
(log_a b)(log_b c)(log_c d)= (log_a b)\frac{log_a c}{log_a b}\frac{log_a d}{log_a c}= log_a d