Basic Log Rules

Front

What is the natural logarithm of a number?

Back

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

Front

What is the relationship between logarithms and exponents?

Back

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

Front

What is the base of the common logarithm?

Back

The base of the common logarithm is 10.

Front

How do you convert from logarithmic form to exponential form?

Back

To convert from logarithmic form log_b(a) = c to exponential form, use the equation b^c = a.

Front

What is the value of ln(e^W)?

Back

The value of ln(e^W) is W.

Front

What is the value of log_10(100)?

Back

The value of log_10(100) is 2, because 10^2 = 100.

Front

Rewrite the equation 3^4 = 81 in logarithmic form.

Back

The logarithmic form is log_3(81) = 4.

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).