Logarithms

Front

What is 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

What is the product rule of logarithms?

Back

The product rule states that log_b(mn) = log_b(m) + log_b(n).

Front

What is the quotient rule of logarithms?

Back

The quotient rule states that log_b(m/n) = log_b(m) - log_b(n).

Front

What is the power rule of logarithms?

Back

The power rule states that log_b(m^n) = n * log_b(m).

Front

How do you express log_4(60) - log_4(4) + log_4(x) as a single logarithm?

Back

log_4(15x) using the product and quotient rules.

Front

What is the value of x in the equation 3^x = 27?

Back

x = 3, since 27 = 3^3.

Front

Evaluate log_3(81).

Back

4, since 81 = 3^4.

Front

How do you express log_5(4) + log_5(3) as a single logarithm?

Back

log_5(12) using the product rule.

Front

Expand the expression log_5(5x^-5).

Back

log_5(5) - 5log_5(x) using the power rule.