4.3-4.5 Flashcard

Front

What is the base of the following logarithm: ln x?

Back

e

Front

Evaluate the following logarithm: log_6 36.

Back

2

Front

Rewrite 3^4 = 81 in logarithmic form.

Back

log_3 81 = 4

Front

Solve the following exponential equation: 5^{-3x} = 125.

Back

x = -1

Front

Solve the following exponential equation: 2^x = 4^{x+1}.

Back

x = -2

Front

What is the definition of a logarithm?

Back

A logarithm is the inverse operation to exponentiation, indicating the power to which a base must be raised to obtain a given number.

Front

What is the change of base formula for logarithms?

Back

log_b a = log_k a / log_k b, where k is any positive number.

Front

What is the relationship between logarithms and exponents?

Back

If b^y = x, then log_b x = y.

Front

What is the value of log_10 100?

Back

2

Front

What is the value of log_2 8?

Back

3