Logarithm Properties and log review

Front

What is the domain of the logarithmic function y = log_b(x)?

Back

(0, ∞) - The logarithmic function is defined for positive real numbers.

Front

What is the range of the logarithmic function y = log_b(x)?

Back

(-∞, ∞) - The output of a logarithmic function can take any real value.

Front

What is the inverse of the exponential function y = b^x?

Back

y = log_b(x) - The logarithm is the inverse operation of exponentiation.

Front

Expand the expression log_b(mn).

Back

log_b(m) + log_b(n) - The logarithm of a product is the sum of the logarithms.

Front

Expand the expression log_b(m/n).

Back

log_b(m) - log_b(n) - The logarithm of a quotient is the difference of the logarithms.

Front

Expand the expression log_b(m^k).

Back

k * log_b(m) - The logarithm of a power is the exponent times the logarithm of the base.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b) - Allows conversion between different logarithmic bases.

Front

If log_b(x) = y, what is the equivalent exponential form?

Back

b^y = x - This shows the relationship between logarithmic and exponential forms.

Front

What is the value of log_b(b)?

Back

1 - The logarithm of a base to itself is always 1.

Front

What is the value of log_b(1)?

Back

0 - The logarithm of 1 in any base is always 0.