Log and Exponential Basics

Front

What is the definition of a logarithm?

Back

A logarithm is the power to which a number must be raised to obtain another number. For example, log_b(a) = c means b^c = a.

Front

What is the relationship between logarithms and exponents?

Back

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

Front

What is the base of a logarithm?

Back

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

Front

What is 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 the base, and x is the exponent.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base of the exponential function is greater than 1 (b > 1), while exponential decay occurs when the base is between 0 and 1 (0 < b < 1).

Front

Solve for x: 2^x = 8.

Back

x = 3.

Front

Rewrite the equation 5^2 = 25 in logarithmic form.

Back

log_5(25) = 2.

Front

What is the value of log_10(1000)?

Back

log_10(1000) = 3.

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. It is denoted as ln(x).

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.