The apparent brightness on Earth of a star is measured on the magnitude scale. The apparent magnitude m of a star is defined by

m = 2.5 log I,

where I is the relative intensity. The accompanying exponential formula is

I = 2.51^m.

To find the relative intensity, we divide the intensity of light from the star Vega by the intensity of light from the star we are studying, with both intensities measured on Earth. Thus, apparent magnitude is a logarithmic function of relative intensity. A certain star has a relative intensity of 3.5, in the sense that on Earth light from Vega is 3.5 times as intense as light from that star.

decimal places.

Note: The magnitude scale is perhaps the reverse of what you might think. The higher the magnitude, the dimmer the star. Some very bright stars have a negative apparent magnitude.

What is the apparent magnitude of the star? Round your answer to two decimal places.