Log Properties

Front

What is the property of logarithms that allows you to condense the expression \( \log_a b - \log_a c \)?

Back

\( \log_a \left( \frac{b}{c} \right) \)

Front

What is the property of logarithms that allows you to expand the expression \( \log_a (bc) \)?

Back

\( \log_a b + \log_a c \)

Front

What is the property of logarithms that allows you to expand the expression \( \log_a (b^n) \)?

Back

\( n \log_a b \)

Front

How do you express the equation \( a^x = b \) in logarithmic form?

Back

\( x = \log_a b \)

Front

What is the change of base formula for logarithms?

Back

\( \log_a b = \frac{\log_c b}{\log_c a} \) for any base \( c \) > 0.

Front

What is the value of \( \log_a a \)?

Back

1, because any number raised to the power of 1 is itself.

Front

What is the value of \( \log_a 1 \)?

Back

0, because any number raised to the power of 0 is 1.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation.

Front

Expand the expression \( \log_2(3y^2) \).

Back

\( \log_2(3) + 2\log_2(y) \)

Front

Expand the expression \( \log_4(6y) \).

Back

\( \log_4(6) + \log_4(y) \)