Logarithms

Front

What is the definition of a logarithm?

Back

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

Front

Convert the logarithmic expression log_b(a) = c to exponential form.

Back

The exponential form is b^c = a.

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

Expand the logarithm: log_b(xy).

Back

log_b(x) + log_b(y).

Front

Condense the expression: log_b(x) + log_b(y).

Back

log_b(xy).

Front

What is the logarithm of 1 in any base?

Back

log_b(1) = 0, because b^0 = 1.

Front

What is the logarithm of the base itself?

Back

log_b(b) = 1, because b^1 = b.

Front

Convert the exponential equation 2^3 = 8 to logarithmic form.

Back

log_2(8) = 3.

Front

If log_b(a) = c, what is the value of a?

Back

a = b^c.

Front

What is the product rule for logarithms?

Back

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