Converting Logs to Exponents

Front

Change to Exponential Form: log₆36 = 2

Back

6² = 36

Front

Solve for x: log_x25 = 2

Back

x = 5

Front

Convert Log_a(100) = 2 to an exponent

Back

a² = 100

Front

Evaluate log₅20 to the third decimal place

Back

1.861

Front

Solve for x: log(x+6) = 1

Back

x = 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

Definition: Base of a Logarithm

Back

The base of a logarithm is the number that is raised to a power to produce a given number.

Front

Definition: Change of Base Formula

Back

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

Front

Example: Convert log₁₀1000 to exponential form

Back

10³ = 1000

Front

Definition: Common Logarithm

Back

A logarithm with base 10, often written as log(x) without a base.