PC CH 9: ENTER Answers for Log and Exp TEST

Front

What is a logarithm?

Back

A logarithm is the power to which a number 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

What is the inverse of a logarithm?

Back

The inverse of a logarithm is an exponentiation. If y = log_b(x), then b^y = x.

Front

How do you graph a logarithmic function?

Back

To graph a logarithmic function, identify key points, such as the x-intercept (1,0) and asymptote (x=0), and plot them.

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is the base, and x is the exponent.

Front

What is the relationship between logarithmic and exponential functions?

Back

Logarithmic functions are the inverses of exponential functions. If y = b^x, then x = log_b(y).

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k.

Front

What is the product rule for logarithms?

Back

The product rule states that log_b(xy) = log_b(x) + log_b(y).

Front

What is the quotient rule for logarithms?

Back

The quotient rule states that log_b(x/y) = log_b(x) - log_b(y).

Front

What is the power rule for logarithms?

Back

The power rule states that log_b(x^k) = k * log_b(x).