6.3 Rewriting Logarithms

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 the logarithmic equation log_2(8) = 3 to exponential form.

Back

2^3 = 8.

Front

What is the value of log_10(1000)?

Back

3, because 10^3 = 1000.

Front

If log_b(x) = y, what is the equivalent exponential form?

Back

b^y = x.

Front

Evaluate log_4(16).

Back

2, because 4^2 = 16.

Front

Solve for x: log_5(x) = 3.

Back

x = 125, because 5^3 = 125.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation.

Front

Convert the logarithmic equation log_6(36) = 2 to exponential form.

Back

6^2 = 36.

Front

If log_8(x) = 2, what is the value of x?

Back

64, because 8^2 = 64.