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. It is expressed as log_b(a) = c, meaning b^c = a.

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(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^k) = k * log_b(x).

Front

How do you convert an exponential equation to a logarithmic equation?

Back

To convert an exponential equation b^c = a to a logarithmic equation, write it as log_b(a) = c.

Front

What is the value of log_4(16)?

Back

The value of log_4(16) is 2, because 4^2 = 16.

Front

What is the value of log_5(25)?

Back

The value of log_5(25) is 2, because 5^2 = 25.

Front

What is the value of log_2(8)?

Back

The value of log_2(8) is 3, because 2^3 = 8.

Front

What is the relationship between logarithms and exponents?

Back

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