Exponential and Logarithmic Functions

Front

What is the definition of an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a(b^x), where a is a constant, b is a positive real number, and x is the exponent.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain another number. For example, in log_b(a) = c, b is the base.

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential functions and logarithmic functions are inverses of each other. If y = b^x, then x = log_b(y).

Front

Evaluate log_5(25).

Back

2

Front

Evaluate log_8(8).

Back

1

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(xy) = log_b(x) + log_b(y).

Front

What is the quotient rule for logarithms?

Back

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

Front

What is the power rule for logarithms?

Back

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

Front

Rewrite log_p(t) = m in exponential form.

Back

p^m = t.