- #1

Callmelucky

- 144

- 30

- Homework Statement
- Write the coordinates of points where ##f(x)=\log _{2} x^2 -1## intersects x and y axis

- Relevant Equations
- ##\log _{a} x^n = n\times \log _{a} x##

So basically this is how I solved this problem:

1. ##f(x)=\log _{2} x^2 - 1##

2. ##0=\log _{2} x^2 -1 ##

3. ##1= 2\times \log _{2} x##

4. ##\frac{1}{2}= \log _{2} x##

5. ##2^{\frac{1}{2}}=x=\sqrt{2}##

So I wrote coordinates to be (##\sqrt{2}##, 0)

But apparently, that is not the only solution. There should be another answer with a negative sign so (##\pm\sqrt{2}##, 0) would be a complete solution for points at which graphs cross the x line. There are no points where the graph crosses the y-line.

This is how it's solved in the textbook(pic in attachments). And I understand that it's correct because the graph really does cross the x-line in those points.

So, my question is, is there a rule I am not aware of that states that I can't divide an equation with n(exponent of an argument moved down to the front)?

Thank you.

1. ##f(x)=\log _{2} x^2 - 1##

2. ##0=\log _{2} x^2 -1 ##

3. ##1= 2\times \log _{2} x##

4. ##\frac{1}{2}= \log _{2} x##

5. ##2^{\frac{1}{2}}=x=\sqrt{2}##

So I wrote coordinates to be (##\sqrt{2}##, 0)

But apparently, that is not the only solution. There should be another answer with a negative sign so (##\pm\sqrt{2}##, 0) would be a complete solution for points at which graphs cross the x line. There are no points where the graph crosses the y-line.

This is how it's solved in the textbook(pic in attachments). And I understand that it's correct because the graph really does cross the x-line in those points.

So, my question is, is there a rule I am not aware of that states that I can't divide an equation with n(exponent of an argument moved down to the front)?

Thank you.

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