{"text": "### Human: Panjang sisi segitiga dengan luas positif adalah log_10(12), log_10(75), dan log_10(n), di mana n adalah bilangan bulat positif. Carilah jumlah nilai yang mungkin untuk n.. ### Assistant: Kita perlu mencari jumlah nilai yang mungkin untuk bilangan bulat positif n, mengingat bahwa panjang sisi segitiga dengan luas positif adalah log_10(12), log_10(75), dan log_10(n. Dengan ketidakadilan segitiga, segitiga yang tidak terdegenerasi dengan panjang sisi ini ada jika dan hanya jika tiga ketidakadilan berikut benar: 1. log_10 75 + log_10 n > log_10 12 2. log_10 12 + log_10 75 > log_10 n 3. log_10 12 + log_10 n > log_10 75 Ketidakadilan pertama selalu benar karena log_1075) > log_1012) dan log_10n) > Ketidakadilan kedua 0.10_12 * 75) > log_10n), yang menyederhanakan ke 900 n. Ketidakadilan ketiga log_10n) memberikan n = 8,85, n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n = n"}