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

Rewrite log_b(x^n)

Back

n log_b(x)

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

log(4x)

Back

log(4) + log(x)

Front

Change to Exponential Form: log_6(36) = 2

Back

6^2 = 36

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

Convert the exponential equation 5^3 = 125 to logarithmic form.

Back

log_5(125) = 3

Front

What is the change of base formula for logarithms?

Back

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