82)

ln(e^4x) = 4x;

1/e^2 = e^-2;

ln(e^-2) = - 2.

4x = -2;

x = - 2/4 = - 1/2.

1/2 = 2^-1;  4 = 2^2;

4^x = 2^-1;

(2^2)^x = 2^-1;

2 ^ 2x = 2 ^ -1;

2x = - 1;

x = - 1/2;

infatti:

4 ^ (-1/2) = (1/4)^1/2 = radice(1/4) = 1/2.

9^x = 1/ (3^3),

(3^2)^x = 3 ^-3;

3^2x = 3 ^ -3;

2x = - 3;

x = - 3/2;

9^(-3/2) = (1/9) ^ 3/2 = [radicequadrata(1/9)]^3 = (1/3)^3 = 1/27.

Sono equazioni elementari.

Si possono ricondurre alla stessa base : a^x = a^q =>  x = q.

82)

e^(4x) = 1/e^2 =>   e^(4x) = e^(-2) => 4x = -2 =>  x = -2/4 = -1/2

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

9^x = 1/27 =>   (3^2)^x = 1/(3^3) =>  3^(2x) = 3^(-3) =>  2x = -3 => x = -3/2.

83)

0.3^x = 0.09 =>  0.3^x = 0.3^2 => x = 2

(1/5)^x = 25 =>   5^(-x) = 5^2 =>  - x = 2 =>  x = -2

[(2/3)^x]^2 = 8/27 => (2/3)^(2x) = (2/3)^3 =>  2x = 3 =>  x = 3/2