Logarithmic Equations

Front

What is a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number. For example, in the expression log_b(a) = c, 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

Convert log_2(8) to exponential form.

Back

2^3 = 8.

Front

Expand the logarithm log_10(100x).

Back

log_10(100) + log_10(x).

Front

Convert the equation 5^(x-1) = 25 to logarithmic form.

Back

log_5(25) = x - 1.

Front

What is the definition of a logarithmic function?

Back

A logarithmic function is the inverse of an exponential function, typically written as f(x) = log_b(x), where b is the base.

Front

What is the asymptote of the function y = log_b(x)?

Back

The vertical asymptote is at x = 0.