PH: L3.3 Properties of Logarithms

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number. For example, if b^y = x, then log_b(x) = y.

Front

What is the product property of logarithms?

Back

The product property states that log_b(MN) = log_b(M) + log_b(N), where M and N are positive numbers.

Front

What is the quotient property of logarithms?

Back

The quotient property states that log_b(M/N) = log_b(M) - log_b(N), where M and N are positive numbers.

Front

What is the power property of logarithms?

Back

The power property states that log_b(M^p) = p * log_b(M), where M is a positive number and p is any real number.

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k, where k ≠ 1.

Front

What is the value of log_10(100)?

Back

log_10(100) = 2, because 10^2 = 100.

Front

What is the value of log_2(8)?

Back

log_2(8) = 3, because 2^3 = 8.

Front

If log_b(25) = 2, what is the value of b?

Back

b = 5, because 5^2 = 25.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation. If b^y = x, then log_b(x) = y.

Front

What is the logarithm of 1 in any base?

Back

log_b(1) = 0 for any base b > 0, because b^0 = 1.