logs to exponents and vice versa

Front

Evaluate the log: log₃(1/9) = ?

Back

-2

Front

How are exponentials and logarithms related?

Back

They're inverses.

Front

Rewrite 3⁴ = 81 in logarithmic form.

Back

log₃81 = 4

Front

Change to Logarithmic Form: 5³ = 125

Back

log₅ 125 = 3

Front

Rewrite log₂8 = 3 in exponential form.

Back

2³ = 8

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number.

Front

If log_b(x) = y, what is the equivalent exponential form?

Back

b^y = x.

Front

What is the base of a logarithm?

Back

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

Front

Convert log₁₀1000 to exponential form.

Back

10³ = 1000.

Front

What is the change of base formula for logarithms?

Back

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