Logs math help

  • #1
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Homework Statement



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

Homework Equations





The Attempt at a Solution



well , the furthest i can reach is

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

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
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965


Since there are no "x" or "y" in the problem I think you are misunderstanding.

"in term so [itex]log_x y[/itex]" simply means "in terms of a single logarithm"

You could, for example, put everything in terms of a logarithm base a:
[tex]log_b c= \frac{log_a c}{log_a b}[/tex]
and
[tex]log_c d= \frac{log_a d}{log_a c}[/tex]
so
[tex](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[/tex]
 
  • #3
438
0


Since there are no "x" or "y" in the problem I think you are misunderstanding.

"in term so [itex]log_x y[/itex]" simply means "in terms of a single logarithm"

You could, for example, put everything in terms of a logarithm base a:
[tex]log_b c= \frac{log_a c}{log_a b}[/tex]
and
[tex]log_c d= \frac{log_a d}{log_a c}[/tex]
so
[tex](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[/tex]

thanks !
 

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