HA2 Logarithms

Front

Write in exponential form: log₂32 = 5

Back

2⁵ = 32

Front

Write in logarithmic form: 2⁻⁴ = 1/16

Back

log₂(1/16) = -4

Front

Evaluate: 3 log₂4

Back

6

Front

Solve for x: logₓ25 = 2

Back

5

Front

Rewrite 3⁴ = 81 in logarithmic form.

Back

log₃81 = 4

Front

Definition: Logarithm

Back

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

Front

Change of Base Formula

Back

logₐb = logₓb / logₓa for any base x.

Front

Definition: Base of a Logarithm

Back

The base of a logarithm is the number that is raised to a power to obtain another number.

Front

Definition: Common Logarithm

Back

A logarithm with base 10, often written as log(x) or log₁₀(x).

Front

Definition: Natural Logarithm

Back

A logarithm with base e (approximately 2.718), written as ln(x).