Natural Log and Power Rule of Log

Front

What is the definition of a logarithm?

Back

A logarithm is the power to which a number (the base) must be raised to obtain another number. For example, if b^y = x, then log_b(x) = y.

Front

What is the natural logarithm?

Back

The natural logarithm is the logarithm to the base e, where e is approximately equal to 2.71828. It is denoted as ln(x).

Front

What is the Power Rule of Logarithms?

Back

The Power Rule states that log_b(a^c) = c * log_b(a). This allows you to bring the exponent in front of the logarithm.

Front

Convert the expression log_2(8) using the Power Rule.

Back

log_2(8) = log_2(2^3) = 3 * log_2(2) = 3.

Front

Write the equation 2^3 = 8 in logarithmic form.

Back

log_2(8) = 3.

Front

Write the equation ln(e^5) in logarithmic form.

Back

ln(e^5) = 5.

Front

What is the relationship between logarithmic and exponential forms?

Back

If log_b(x) = y, then it can be rewritten in exponential form as b^y = x.

Front

Convert the expression log_10(100) to exponential form.

Back

10^2 = 100.

Front

What is the base of a logarithm?

Back

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

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.