Properties of Logs and Solving Logs

Front

What is the product property of logarithms?

Back

log_b(MN) = log_b(M) + log_b(N) for any positive numbers M and N.

Front

What is the quotient property of logarithms?

Back

log_b(M/N) = log_b(M) - log_b(N) for any positive numbers M and N.

Front

What is the power property of logarithms?

Back

log_b(M^p) = p * log_b(M) for any positive number M and any real number p.

Front

Expand: log_b(M^p)

Back

p * log_b(M) using the power property.

Front

Condense: log_b(M) + log_b(N)

Back

log_b(MN) using the product property.

Front

Condense: log_b(M) - log_b(N)

Back

log_b(M/N) using the quotient property.

Front

What is the change of base formula for logarithms?

Back

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

Front

If log_b(x) = p, what is x in terms of b and p?

Back

x = b^p.

Front

Solve for x: log_5(4x - 7) = log_5(x + 5)

Back

x = 4.

Front

What is the value of log_b(b)?

Back

log_b(b) = 1 for any base b.