SOLUTION: log base x (w)=24, log base y (w)=40, log base xyz (w)=12. Find log base z (w).

Question 1111152: log base x (w)=24, log base y (w)=40, log base xyz (w)=12. Find log base z (w).
Answer by ikleyn(52847) (Show Source): You can put this solution on YOUR website!
.

You are given

 = 24,      (1)

 = 40,      (2)

 = 12.    (3)



(1) is equivalent to    = w,          (1')

(2) is equivalent to    = w,          (2')

(3) is equivalent to    = w.       (3')


From (3')    = ,   or    = .    (4)


Replace here   by   based on (1').   Replace    by ,  based on (2').  Then you will get


 = ,    which implies

 =   and then   = w.


The last equality means that   = 60.


Answewr.   = 60.

Solved.

--------------
On logarithms and their properties, see the lessons
    - WHAT IS the logarithm
    - Properties of the logarithm
    - Change of Base Formula for logarithms
    - Solving logarithmic equations
    - Using logarithms to solve real world problems
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Logarithms".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

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