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

August 27, 2021 | education

| 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.

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