Find the root of the equation log log x-5 49 = 2 If your equation has more than one root, answer the smaller one.

Let’s analyze ODZ (range of acceptable values), the base of the logarithm must be greater than zero and not equal to one.

x – 5 is not equal to 1; x is not equal to 6.

x – 5> 0; x> 5.

We solve the equation:

log (x – 5) 49 = 2.

(x – 5) ² = 49;

x² – 10x + 25 – 49 = 0;

x² – 10x – 24 = 0.

Solve the quadratic equation using the discriminant.

a = 1; b = -10; c = -24.

D = b² – 4ac = (-10) ² – 4 * (-24) = 100 + 96 = 196 (√D = 14);

x1 = (10 – 14) / 2 = -4/2 = -2 (not suitable for ODZ).

x2 = (10 + 14) / 2 = 24/2 = 12.

Answer: The root of the equation is 12.