7.6 Properties of Logs

Front

What is the property of logarithms that allows you to write log_b(x/y) as two logs?

Back

log_b(x) - log_b(y)

Front

Convert the logarithmic equation log_6(36) = 2 to exponential form.

Back

6^2 = 36

Front

Use logarithmic properties to combine log_2(x) - 5log_2(y) into a single logarithm.

Back

log_2(x/y^5)

Front

What are logarithmic functions the inverse of?

Back

Exponential Functions

Front

Simplify the expression log(m^3/n).

Back

3log(m) - log(n)

Front

What is the change of base formula for logarithms?

Back

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

Front

What is the product property of logarithms?

Back

log_b(xy) = log_b(x) + log_b(y) for any positive x and y.

Front

What is the quotient property of logarithms?

Back

log_b(x/y) = log_b(x) - log_b(y) for any positive x and y.

Front

What is the power property of logarithms?

Back

log_b(x^k) = k * log_b(x) for any positive x and k.

Front

If log_b(x) = p, what is the value of x in exponential form?

Back

x = b^p