Laws of Logarithms

Front

Write 2^3= 8 in logarithmic form.

Back

log_2 8 = 3

Front

Evaluate log_7 343.

Back

3

Front

The common logarithm has what base?

Back

10

Front

Solve for x: log_x 25 = 2.

Back

5

Front

Rewrite log_2 8 = 3 in exponential form.

Back

2^3 = 8

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.

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.

Front

What is the product rule of logarithms?

Back

log_b (xy) = log_b x + log_b y.

Front

What is the quotient rule of logarithms?

Back

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