Logarithm Properties and log review

Front

What is the property of logarithms that allows you to condense the expression log_b(x) - log_b(y)?

Back

log_b(x/y) - This property states that the difference of two logarithms with the same base can be expressed as the logarithm of the quotient.

Front

What is the property of logarithms that allows you to condense the expression log_b(x) + log_b(y)?

Back

log_b(xy) - This property states that the sum of two logarithms with the same base can be expressed as the logarithm of the product.

Front

What is the property of logarithms that allows you to express k * log_b(x)?

Back

log_b(x^k) - This property states that a constant multiplied by a logarithm can be expressed as the logarithm of the base raised to the power of that constant.

Front

What is the value of log₁₀(10)?

Back

1 - The logarithm of a number to its own base is always 1.

Front

What is the value of log₁₀(1)?

Back

0 - The logarithm of 1 to any base is always 0.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_c(a) / log_c(b) - This formula allows you to convert logarithms from one base to another.

Front

Evaluate the expression: log₂(8).

Back

3 - Since 2³ = 8, log₂(8) = 3.

Front

Evaluate the expression: log₃(1/27).

Back

-3 - Since 3^-3 = 1/27, log₃(1/27) = -3.

Front

What is the result of simplifying the expression: log₅(25)?

Back

2 - Since 5² = 25, log₅(25) = 2.

Front

What is the result of simplifying the expression: log₄(16)?

Back

2 - Since 4² = 16, log₄(16) = 2.