M3 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, 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 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^p) = p * log_b(m).

Front

How do you solve the equation log_b(x) = c for x?

Back

To solve log_b(x) = c, rewrite it in exponential form: x = b^c.

Front

What is the domain of a logarithmic function?

Back

The domain of a logarithmic function is the set of positive real numbers, as the logarithm of zero or a negative number is undefined.

Front

What is the relationship between logarithms and exponents?

Back

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

Front

How can you express log_8(9) in terms of natural logarithms?

Back

log_8(9) = ln(9) / ln(8) using the change of base formula.

Front

What is the significance of the base in a logarithmic equation?

Back

The base of a logarithm determines the rate of growth of the logarithmic function and affects the shape of its graph.