# Example 1

You know that Arcturus’s g-r color is 1.06. By the definition of color:

`g-r = Mag`

_{g} - Mag_{r}.

And by the definition of magnitude,

`g-r = -log`

_{2.51} (F_{green}) + log_{2.51} (F_{red}) = 1.06.

Switch the order of the logarithms to get log_{2.51} (F_{red}) – log_{2.51} (F_{green}) = 1.06.

Using the rule of logarithms that log (x) – log (y) = log (x/y), you know that:

`log`

_{2.51} (F_{red} / F_{green}) = 1.06.

Invert the log by raising 2.51 to the power of both sides of the equation; that is,

`2.51 ^ [log`

_{2.51} (F_{red} / F_{green})] = 2.51^{1.06}

The log is cancelled on the left side of the equation, meaning:

`F`

_{red} / F_{green} = 2.51^{1.06}.

To solve for F_{red}, get F_{red} alone on the left side of the equation:

`F`

_{red} = (2.51^{1.06})F_{green}.

Use a calculator to find that the coefficient is about 2.65.

Therefore, Arcturus gives off 2.65 times as much red light as green light.