Log graph Relationship

[eutas1]

I have NO idea how to even attempt this question (please refer to attachment). I don't even think I understand the question itself - what does it mean linear relationship??? Is it saying the y-axis is log27(y) and that the x-axis is log9(x) ????

Note: This is a calculator-free question.

 

[Harry_the_cat]

Yes the horizontal axis is \(\displaystyle \log_9(x)\) and the vertical axis is \(\displaystyle \log_{27}(y)\).

I can see two ways to proceed.

Do you know that a linear (ie straight-line) log-log graph can be expressed as a power function, ie in the form \(\displaystyle y=Ax^b\)?

 

[Dr.Peterson]

I have NO idea how to even attempt this question (please refer to attachment). I don't even think I understand the question itself - what does it mean linear relationship??? Is it saying the y-axis is log27(y) and that the x-axis is log9(x) ????

Note: This is a calculator-free question.

I might start by defining the actual coordinates on the graph as [imath]u=\log_9(x)[/imath] and [imath]v=\log_{27}(y)[/imath]. Then write the equation of the line, relating u and v.