Logarithmic Equations

Front

What is the definition of a logarithm?

Back

A logarithm is the power to which a number (the base) must be raised to obtain another number. For example, log_b(a) = c means 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 rule of logarithms?

Back

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

Front

What is the quotient rule of logarithms?

Back

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

Front

What is the power rule of logarithms?

Back

The power rule states that log_b(x^k) = k * log_b(x).

Front

How do you convert a logarithmic equation to exponential form?

Back

To convert log_b(a) = c to exponential form, rewrite it as b^c = a.

Front

What is the value of log_10(1000)?

Back

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

Front

Solve for x: log_2(x) = 5.

Back

x = 32 because 2^5 = 32.

Front

What is the value of log_4(64)?

Back

log_4(64) = 3 because 4^3 = 64.

Front

If log_b(x) = 0, what is the value of x?

Back

x = 1 because b^0 = 1.