Logarithms

Front

What is a logarithm?

Back

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

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 the logarithmic identity for log_b(1)?

Back

log_b(1) = 0, because any number raised to the power of 0 equals 1.

Front

What is the logarithmic identity for log_b(b)?

Back

log_b(b) = 1, because any number raised to the power of 1 equals itself.

Front

How do you convert from exponential form to logarithmic form?

Back

If b^c = a, then log_b(a) = c.

Front

What is the product rule of logarithms?

Back

log_b(xy) = log_b(x) + log_b(y).

Front

What is the quotient rule of logarithms?

Back

log_b(x/y) = log_b(x) - log_b(y).

Front

What is the power rule of logarithms?

Back

log_b(x^k) = k * log_b(x).

Front

Evaluate: log_6(1/216)

Back

-3, because 6^(-3) = 1/216.

Front

Expand: log_8(xy^5z)

Back

log_8(x) + 5*log_8(y) + log_8(z).