Basic Log Rules

Front

What is the base of the common logarithm?

Back

10

Front

Evaluate log₃81 without a calculator.

Back

4

Front

Rewrite in exponential form: 2=log₉x

Back

9²=x

Front

Solve for x: log₄x = 3 without a calculator.

Back

64

Front

Evaluate log_b(b).

Back

1

Front

What is the change of base formula for logarithms?

Back

log_a(b) = log_c(b) / log_c(a) for any base c.

Front

If log_a(b) = c, what is the equivalent exponential form?

Back

a^c = b.

Front

What is the logarithm of 1 in any base?

Back

0, because log_a(1) = 0 for any a > 0.

Front

What is the logarithm of the base itself?

Back

1, because log_a(a) = 1 for any a > 0.

Front

Evaluate log₁₀(1000).

Back

3, because 10³ = 1000.