Properties of Logs

Front

When you have two log expressions separated by a minus sign (-), we really need to ___________ them to simplify into one log expression.

Back

divide

Front

Use multiple log properties to write as a single log: log₂x - 5log₂y

Back

log₂(x/y⁵)

Front

Write log_b(x/y) as two logs.

Back

log_b(x) - log_b(y)

Front

When you have two log expressions separated by a plus sign (+), we really need to ___________ them to simplify into one log expression.

Back

multiply

Front

Simplify: 2log(x) + 3log(xy)

Back

log(x⁵y³)

Front

What is the product property of logarithms?

Back

log_b(MN) = log_b(M) + log_b(N)

Front

What is the quotient property of logarithms?

Back

log_b(M/N) = log_b(M) - log_b(N)

Front

What is the power property of logarithms?

Back

log_b(M^p) = p * log_b(M)

Front

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

Back

M = b^p

Front

What is the change of base formula for logarithms?

Back

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