Logarithms

Front

What is a logarithm?

Back

A logarithm is the power to which a number (the base) must be raised to obtain another number. For example, log_b(a) = c means b^c = a.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power. In log_b(a), b is the base.

Front

Evaluate: log_6(1/216)

Back

-3

Front

Expand: 5log_5(a) - 6log_5(b)

Back

5log_5(a) - 30log_5(b)

Front

What transformation does y = log(x + 3) represent?

Back

Left 3.

Front

In the general log function y = a*log_b(x - h) + k, what does 'h' represent?

Back

The horizontal shift of the graph; it indicates if the function has moved left or right.

Front

Evaluate: log_3(81)

Back

4

Front

What is the change of base formula for logarithms?

Back

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

Front

What is the product rule for logarithms?

Back

log_b(m * n) = log_b(m) + log_b(n).

Front

What is the quotient rule for logarithms?

Back

log_b(m / n) = log_b(m) - log_b(n).