[Astrophysics] Star luminosity-radius-temperature problem

[Andrev]

Hi!

Homework Statement

The light variation of a Cepheid is 2 mag,if its effective temperature at maximum luminosity is
6000K, while at minimum is 5000K, please estimate the ratio of its maximum and minimum
radius.

Homework Equations

$$\Delta m=-2,5lg\frac{L_{min}}{L_{max}}$$
$$lg\frac{L_{min}}{L_{max}}=2lg\frac{R_{min}}{R_{max}}+4lg\frac{L_{min}}{L_{max}}$$

The Attempt at a Solution

Well, actually I should solve the problem with those two formulas above. My question is: why I can not just calculate the $$\frac{L_{min}}{L_{max}}$$ and solve the $$\frac{L_{min}}{L_{max}}=\frac{4\pi R_{min}^2 \cdot T_{min}^4\cdot \sigma}{4\pi R_{max}^2 \cdot T_{max}^4\cdot \sigma}$$ equation? Why I have to calculate with the lgs? As I studied the problem it looked for me that these two methods are equal but I got different results.

Thanks in advance,


Andrev

 

[Andrev]

Sorry for spamming the forum with this I solved it on my own:

Of course I can calculate with the form without lgs too. I missed the calculation at the beginning: I forgot that the magnitude scale is inverse, so $$-0.4\cdot (m_1-m_2)=-0.4 \cdot \Delta m <0$$ It is ok now. Andrev