Natural Logs

Front

What is the natural logarithm of a number?

Back

The natural logarithm of a number is the logarithm to the base e, where e is approximately equal to 2.71828.

Front

How do you rewrite an exponential equation in logarithmic form?

Back

To rewrite an exponential equation in logarithmic form, use the formula: if a^b = c, then log_a(c) = b.

Front

What is the base of the natural logarithm?

Back

The base of the natural logarithm is e.

Front

What is the notation for the natural logarithm?

Back

The notation for the natural logarithm is ln.

Front

How do you solve the equation ln(x) = a for x?

Back

To solve the equation ln(x) = a for x, rewrite it in exponential form: x = e^a.

Front

What is the value of e raised to the power of 0?

Back

The value of e raised to the power of 0 is 1.

Front

What is the derivative of the natural logarithm function?

Back

The derivative of the natural logarithm function ln(x) is 1/x.

Front

What is the integral of the natural logarithm function?

Back

The integral of ln(x) is x ln(x) - x + C, where C is the constant of integration.

Front

How do you expand the natural logarithm of a quotient?

Back

The natural logarithm of a quotient can be expanded using the property: ln(a/b) = ln(a) - ln(b).

Front

How do you expand the natural logarithm of a power?

Back

The natural logarithm of a power can be expanded using the property: ln(a^b) = b ln(a).