Finding Logs

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, in the expression log_b(a) = c, 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 relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation. If b^c = a, then log_b(a) = c.

Front

Evaluate log_6(36) without a calculator.

Back

log_6(36) = 2 because 6^2 = 36.

Front

What is the value of log_125(25)?

Back

log_125(25) = 2/3 because 125^(2/3) = 25.

Front

Convert the logarithmic equation log_6(216) = 3 to exponential form.

Back

6^3 = 216.

Front

What does it mean if log_b(a) is undefined?

Back

log_b(a) is undefined if a <= 0 or b <= 0 or b = 1.

Front

Rewrite the equation log_x(95) = 2.3 in exponential form.

Back

x^2.3 = 95.

Front

What is the value of log_6(-36)?

Back

Not possible, as logarithms of negative numbers are undefined.

Front

How do you express 6^3 = 216 as a logarithm?

Back

log_6(216) = 3.