Converting Logs to Exponents

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

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation.

Front

Convert Log₂(64) = y to an exponent.

Back

2^y = 64.

Front

What is the value of y in the equation Log₂(64) = y?

Back

y = 6, because 2⁶ = 64.

Front

Convert Log_a(100) = 2 to an exponent.

Back

a² = 100.

Front

What is the value of a in the equation Log_a(100) = 2?

Back

a = 10, because 10² = 100.

Front

Convert Log₃(x) = 4 to an exponent.

Back

3⁴ = x.

Front

What is the value of x in the equation Log₃(x) = 4?

Back

x = 81, because 3⁴ = 81.

Front

Solve for x: log_x25 = 2.

Back

x = 5, because 5² = 25.

Front

What is the change of base formula for logarithms?

Back

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