Question

Решите уравнение a) √3 умножить 3^2x = 1/9 , б) 5^x - 7.5^x-2 = 90

Answer 1

а) √3 * 3^2x = 1/9

3^½ * 3^2x = 3^-2

3^(½ + 2x)/3^-2 = 1

3^(4x - 4/2) = 1

9^(x - 1) = 1

9^x/9 = 1

9^x = 9

x = log⁹9 = 1

б) 5^x - 7*5^(x-2) = 90

5^x - 7 * 5^x /25 = 90

5^x * (1 - 7/25) = 90

5^x * (18/25) = 90

5^x = 90 * 25/ 18

5^x = 125

x = log⁵125 = 3