Simplifying Logarithmic Expressions to \log_x{y}

[thereddevils]

Homework Statement

Simplify (\log_a{b})(\log_b{c})(\log_c{d}) in terms of \log_x{y}

Homework Equations

The Attempt at a Solution

well , the furthest i can reach is

\frac{\log_xd}{\log_xa} , how do i express in terms of \log_x{y}

 

[HallsofIvy]

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

 

[thereddevils]

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

thanks !