Q.Crape myrtle leaves turning brown on ends with tiny white areas
15 gallon Crapes planted in early April of this year. Variety is Tonto. Blooming well. Deep hand water twice a week. Garden is sprinkled once per week. Temps in August 95-100.
Spider mites or not enough water?
White patches could be spider mites or powdery mildew. More information here: https://www.gardeningknowhow.com/plant-problems/pests/insects/spider-mite-treatment.htm
The browning may well be a stress reaction to high summer heat, plus this is a newly planted tree. You can check the water by digging with a hand trowel - after watering, ground should be moist at least 6" deep. You can check in the middle of the week, if the soil is dry, you can water again.