Exponential and Logarithmic Functions Practice Test

Front

What is the value of log₄1?

Back

0

Front

What is the base of a logarithm in the expression log_b(x)?

Back

The base 'b' is the number that is raised to a power to obtain x.

Front

How do you solve the equation log₆x + log₆(x-5) = 2?

Back

Combine the logs: log₆(x(x-5)) = 2, then convert to exponential form: x(x-5) = 6², leading to x = 9.

Front

What is the product property of logarithms?

Back

log_b(xy) = log_b(x) + log_b(y) for any positive x and y.

Front

What is the quotient property of logarithms?

Back

log_b(x/y) = log_b(x) - log_b(y) for any positive x and y.

Front

How can you express log(4x³) using properties of logarithms?

Back

log(4x³) = log 4 + 3log x.

Front

What is the change of base formula for logarithms?

Back

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

Front

How do you solve log₆(3x - 2) = log₆(5x - 8)?

Back

Set the arguments equal: 3x - 2 = 5x - 8, leading to x = 3.

Front

What is the definition of a logarithm?

Back

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

Front

What is the value of log_b(b)?

Back

1, because b¹ = b.