Properties of Logarithms

Front

Write log_b(xy) as two logs

Back

log_b(x) + log_b(y)

Front

Write the expression as a single logarithm: log_5(3) + log_5(6) + log_5(9)

Back

log_5(162)

Front

Rewrite log_b(x^n)

Back

n * log_b(x)

Front

Write the expression as a single logarithm: log(6) - log(3) + 2 * log(7)

Back

log(98)

Front

Condense: log(x) + log(y) + log(z^3)

Back

log(xyz^3)

Front

What is the product property of logarithms?

Back

log_b(xy) = log_b(x) + log_b(y)

Front

What is the quotient property of logarithms?

Back

log_b(x/y) = log_b(x) - log_b(y)

Front

What is the power property of logarithms?

Back

log_b(x^n) = n * log_b(x)

Front

If log_b(a) = c, what is the equivalent exponential form?

Back

b^c = a

Front

What is the change of base formula for logarithms?

Back

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