Log Properties

Front

Rewrite in exponential form: log_9(x) = 2

Back

9^2 = x

Front

Expand log_4(6y)

Back

log_4(6) + log_4(y)

Front

Write as a logarithm: 4^x = 64

Back

log_4(64) = x

Front

Expand log_4(3xy)

Back

log_4(3) + log_4(x) + log_4(y)

Front

Expand: log_2(5/x)

Back

log_2(5) - log_2(x)

Front

Definition of a logarithm

Back

A logarithm is the exponent to which a base must be raised to produce a given number.

Front

Change of base formula for logarithms

Back

log_b(a) = log_k(a) / log_k(b) for any base k.

Front

Product property of logarithms

Back

log_b(mn) = log_b(m) + log_b(n) for any positive m and n.

Front

Quotient property of logarithms

Back

log_b(m/n) = log_b(m) - log_b(n) for any positive m and n.

Front

Power property of logarithms

Back

log_b(m^p) = p * log_b(m) for any positive m and p.