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, log_b(a) = c means b^c = a.

Front

What is the product property of logarithms?

Back

The product property states that log_b(xy) = log_b(x) + log_b(y).

Front

What is the quotient property of logarithms?

Back

The quotient property states that log_b(x/y) = log_b(x) - log_b(y).

Front

What is the power property of logarithms?

Back

The power property states that log_b(x^n) = n * log_b(x).

Front

Convert log_2(32) = 5 to exponential form.

Back

2^5 = 32.

Front

Condense the expression: log_6 - log_3 + 2 log_7.

Back

log(6/3) + log(7^2) = log(2) + log(49) = log(2*49) = log(98).

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.

Front

If log_b(x) = 3, what is the value of x?

Back

x = b^3.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation.

Front

What is the base of a common logarithm?

Back

The base of a common logarithm is 10.