Logs to Exponents

Front

What is the definition of a logarithm?

Back

A logarithm is the power to which a number (the base) must be raised to obtain another number.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation.

Front

Rewrite log_bA = x in exponential form.

Back

A = b^x

Front

What does the base in a logarithmic function represent?

Back

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

Front

Convert the exponential equation 2³ = 8 into logarithmic form.

Back

log₂8 = 3

Front

If log₁₀100 = x, what is the value of x?

Back

x = 2, because 10² = 100.

Front

What is the change of base formula for logarithms?

Back

log_bA = log_kA / log_kb for any base k.

Front

Rewrite the equation 5^x = 25 in logarithmic form.

Back

log₅25 = x

Front

What is the value of log₃27?

Back

log₃27 = 3, because 3³ = 27.

Front

If log₄x = 2, what is the value of x?

Back

x = 16, because 4² = 16.