The sum of the first n terms of a harmonic progression diverges as n approaches infinity, hence it is not finite.

The last statement is incorrect as it does not follow the properties of logarithms.

Modular arithmetic is commutative for addition and multiplication, hence non-commutativity is not a property.

Polygons are defined as shapes made up of straight line segments, so having curved sides disqualifies a shape from being a polygon.

Not all triangles have all angles acute; for example, a right triangle has one angle that is 90 degrees.

'22' cannot represent 10 in any base since it would require base 3 or higher.

A factor is defined as a number that divides another number without leaving a remainder.

The quadratic x^2 - 5x + 6 factors to (x - 2)(x - 3).

All the listed properties are correct and fundamental to logarithmic functions.

The decimal number 15 is represented as '1111' in binary.

Using the power of a product property, (a*b)^n = a^n * b^n, we get (x^3)^2 * (y^2)^2 = x^6 * y^4.

Using the property of logarithms, log_2(8) + log_2(4) = log_2(8*4) = log_2(32) = log_2(16).

log_5(25) = 2 and log_5(5) = 1, thus log_5(25) - log_5(5) = 2 - 1 = 1.

The GCD of 48 and 180 is 12, as it is the largest number that divides both without a remainder.

Using the power of a power property, (a^m)^n = a^(m*n), we get (2^3)^2 = 2^(3*2) = 2^6.

The polynomial can be factored as (x + 2)^2, indicating it has one real root with multiplicity 2.

Using the property of exponents, we have 2^(x+1 - (x-1)) = 2^(x+1-x+1) = 2^2.

Since 16 can be expressed as 4^2, we have 4^(x+1) = 4^2, leading to x + 1 = 2, thus x = 1.

Since 0.01 is 10^-2, log_10(0.01) = -2.

Logarithm of zero is undefined, hence log_5(0) is the correct answer.

12 is the smallest number that is a multiple of both 4 and 6.

The LCM of 8 and 12 is 24, which is a multiple of both.

121 is divisible by 11, as 121 = 11 x 11.

A number is divisible by 8 if the last three digits form a number that is divisible by 8. 64 is divisible by 8.

55 is not divisible by 12, as it does not meet the criteria of being divisible by both 3 and 4.

A number is divisible by 3 if the sum of its digits is divisible by 3. The sum of the digits of 22 (2 + 2 = 4) is not divisible by 3.

Complementary angles are two angles whose sum is 90 degrees. All the given pairs meet this criterion.

Supplementary angles are two angles that add up to 180 degrees. An acute angle (less than 90 degrees) and an obtuse angle (more than 90 degrees) can add up to 180 degrees.

The first pair has the same slope (2/3) and thus represents parallel lines.

The first pair represents parallel lines, which means they will never intersect, hence no solution.