Solving Logarithmic 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, in the equation log_b(a) = c, b^c = a.

Front

What is the base of the common logarithm?

Back

The base of the common logarithm is 10.

Front

Solve for x: log_8(4x + 4) = 2.

Back

x = 15.

Front

What is the natural logarithm?

Back

The natural logarithm is the logarithm to the base e, where e is approximately equal to 2.718.

Front

If log_x(1000) = 3, what is x?

Back

x = 10.

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 for logarithms?

Back

The product rule states that log_b(mn) = log_b(m) + log_b(n).

Front

What is the quotient rule for logarithms?

Back

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

Front

What is the power rule for logarithms?

Back

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

Front

How do you solve logarithmic equations?

Back

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