Finding the Unknown Variable in a System of Linear Equations

[chwala]

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...

 

[Mark44]

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 $\sqrt{}$?

 

[chwala]

sorry let me amend the question...

 

[chwala]

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

 

[PeroK]

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]

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...