Since 8 is 2^3, log_2(8) equals 3.

log_2(x) + 2 = 5 implies log_2(x) = 3, thus x = 2^3 = 8.

Since 27 is 3^3, log_3(27) = 3.

The expression log_a(b) = c can be rewritten in exponential form as a^c = b.

The definition of logarithms states that if log_a(b) = c, then a raised to the power of c equals b, hence a^c = b.

By the definition of logarithms, if log_a(b) = x, then b = a^x.

The definition of logarithms states that if log_b(x) = y, then b raised to the power of y equals x, hence b^y = x.

The logarithm of a product is indeed the sum of the logarithms, as per the property log(a*b) = log(a) + log(b).

The property of logarithms states that the sum of logarithms with the same base is equal to the logarithm of the product, thus log_a(b) + log_a(c) = log_a(bc).

The base of the logarithm is 10, as log_10(100) = 2 means 10^2 = 100.

Since 8 is 2 raised to the power of 3 (2^3 = 8), the base of the logarithm is 2.

Since 81 is 3^4, the base of the logarithm is 3.

For any base b > 0, log_b(1) = 0, since b^0 = 1.

Logarithms are primarily used to simplify multiplication and division into addition and subtraction, making calculations easier.

log_10(0.1) = log_10(10^-1) = -1.

log_2(8) = 3 and log_2(4) = 2, thus log_2(8) + log_2(4) = 3 + 2 = 5.

log_10(0.01) can be rewritten as log_10(10^-2) = -2.

log_10(1/100) = log_10(10^-2) = -2.

log_10(100) = 2 and log_10(10) = 1, so 2 + 1 = 3.

Since 1000 is 10^3, log_10(1000) = 3.

Using the property of logarithms, log_5(25) = 2 and log_5(5) = 1. Therefore, log_5(25) + log_5(5) = 2 + 1 = 3, which is log_5(125).

Since 1000 is 10^3, log_10(1000) equals 3.

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

The base of the natural logarithm is e, approximately equal to 2.718.

log_5(1) = 0 because any number raised to the power of 0 equals 1.

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

log_10(1000) = 3 and log_10(0.01) = -2, thus 3 + (-2) = 1.

Using the property of logarithms, log_10(1000) = 3 and log_10(10) = 1. Therefore, log_10(1000) - log_10(10) = 3 - 1 = 2.

log_10(1000) = log_10(10^3) = 3.

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