Solving Basic Log Equations

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 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(m * n) = log_b(m) + log_b(n).

Front

What is the quotient rule of logarithms?

Back

The quotient rule states that log_b(m / n) = log_b(m) - log_b(n).

Front

What is the power rule of logarithms?

Back

The power rule states that log_b(m^n) = n * log_b(m).

Front

Solve for x: log_x(1000) = 3

Back

x = 10.

Front

If log_4(3x - 1) = log_4(2x + 3), what is x?

Back

x = 4.

Front

Solve for x: log_2(x) = 4

Back

x = 16.

Front

Solve for x: log_5(x) = 0

Back

x = 1.

Front

What is the definition of a base in logarithms?

Back

The base of a logarithm is the number that is raised to a power to obtain a certain value. In log_b(a), b is the base.