# Solving a logarithm problem

Gold Member

## Homework Statement:

let ##x,y,z>1##, and ##m>1## so that ##log_{xy}m=9##

##log_{yz}m=18##

##log_{xyz}m=8##

find ##log_{xz}m##

## Relevant Equations:

logarithms

this is my working....

## Answers and Replies

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Mark44
Mentor
Homework Statement:: let ##x,y,z>1##, and ##m>1## so that ##log_{xy}m=9##

##log_{yz}m=18##

##log_{xyz}m=8##

find ##log_{xz}##
Relevant Equations:: logarithms

View attachment 265398

this is my working....
find ##log_{xz}##
The problem statement is incomplete. ##\log_{xy}## of what?
This is like asking what is ##\sqrt{}##?

Gold Member
sorry let me amend the question...

Gold Member
find ##log_{xz}m##....i checked with my colleague, my solution is correct, i would be looking at probably an alternative approach. thanks

PeroK
Homework Helper
Gold Member
find ##log_{xz}m##....i checked with my colleague, my solution is correct, i would be looking at probably an alternative approach. thanks
You can transform this into a set of linear equations:
$$9x + 9y = 1, \ \ \ 18y + 18z = 1, \ \ \ 8x + 8y + 8z = 1$$
And you want to find ##a## such that:
$$ax + az = 1$$

chwala
Gold Member
You can transform this into a set of linear equations:
$$9x + 9y = 1, \ \ \ 18y + 18z = 1, \ \ \ 8x + 8y + 8z = 1$$
And you want to find ##a## such that:
$$ax + az = 1$$
let me check this out...