why do my tomatoes have brown spots on the bottom

This is probably blossom end rot. It occurs at the bottom of the tomato and sort of looks like a bruise that may or may not be indented somewhat. Crushed egg shells in the dirt will replace a calcium shortage which is frequently the cause.

Also, too much water and/or fertilizer (indicated particularly if you have plants that are very tall but not bearing much fruit) can cause blossom end rot.

Pick the affected fruit as soon as you notice the problem so the plant s energy is spent on healthy fruit instead. Usually only affects some of the fruit on a plant, and most often only the first fruits.
This brown/black spot is called BER (blossom end rot), caused by a calcium deficiency within the fruit of the plant.

Utah soils have plenty of calcium, but for some reason calcium was not translocated during early fruit set.

Failure to translocate calcium occurs during times of stress: transplanting, cool cloudy weather, root rot, or drought. Soil enriched with high quality organic matter reduces BER because it retains moisture while also providing aeration to roots.

Mulch helps prevent BER by reducing swings in soil moisture, plus it sustains soil organic matter for good aeration.