7.4 Expanding/Condensing Logs

Front

What is the exponential form of log_v(n) = a?

Back

v^a = n

Front

How do you expand log(4x)?

Back

log(4x) = log(4) + log(x)

Front

What is the value of log_x(25) = 2?

Back

x = 5

Front

How do you condense log(xy^2)?

Back

log(xy^2) = log(x) + 2*log(y)

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

Front

What is the power property of logarithms?

Back

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

Front

How do you convert an exponential equation to logarithmic form?

Back

If b^y = x, then log_b(x) = y.

Front

What is the definition of a logarithm?

Back

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