Log Basics

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b) for any base k.

Front

Evaluate log_4(32) using the change of base formula.

Back

5/2

Front

Rewrite log_3(64) using the change of base formula.

Back

log(64)/log(3)

Front

If x = 11^y, how can this be rewritten as a logarithm?

Back

log_11(x) = y

Front

Convert log_6(216) = 3 into exponential form.

Back

6^3 = 216

Front

Solve for x: log_x(25) = 2.

Back

5

Front

What does log_b(a) represent?

Back

The exponent to which the base b must be raised to produce a.

Front

If log_10(100) = x, what is the value of x?

Back

2, because 10^2 = 100.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation.

Front

How do you express log_a(b) in terms of natural logarithms?

Back

log_a(b) = ln(b) / ln(a).