Log Practice #1

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. For example, log_b(a) = c means b^c = a.

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k.

Front

Convert log_2(16) to exponential form.

Back

2^4 = 16.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation.

Front

Rewrite the equation 5^x = 25 in logarithmic form.

Back

log_5(25) = x.

Front

What is the value of log_10(1000)?

Back

3, because 10^3 = 1000.

Front

If log_a(b) = c, what is b in terms of a and c?

Back

b = a^c.

Front

Convert log_3(81) to exponential form.

Back

3^4 = 81.

Front

What is the product rule for logarithms?

Back

log_b(m * n) = log_b(m) + log_b(n).

Front

What is the quotient rule for logarithms?

Back

log_b(m / n) = log_b(m) - log_b(n).