Solving Logs using Properties Shortened

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 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

What is the product property of logarithms?

Back

The product property states that log_b(MN) = log_b(M) + log_b(N). This means the logarithm of a product is the sum of the logarithms.

Front

What is the quotient property of logarithms?

Back

The quotient property states that log_b(M/N) = log_b(M) - log_b(N). This means the logarithm of a quotient is the difference of the logarithms.

Front

What is the power property of logarithms?

Back

The power property states that log_b(M^p) = p * log_b(M). This means the logarithm of a number raised to a power is the power times the logarithm of the number.

Front

How do you solve log equations?

Back

To solve log equations, isolate the logarithm, convert to exponential form, and then solve for the variable.

Front

What is the definition of a common logarithm?

Back

A common logarithm is a logarithm with base 10, denoted as log(x) or log_10(x).

Front

What is the definition of a natural logarithm?

Back

A natural logarithm is a logarithm with base e (approximately 2.718), denoted as ln(x).

Front

How do you evaluate log_10(1000)?

Back

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

Front

How do you evaluate ln(e^5)?

Back

ln(e^5) = 5, because the natural logarithm and the exponential function are inverses.