Ch 3 Test Review

Front

What is the logarithmic form of the equation 5^{x-2}=13?

Back

The logarithmic form is x-2 = log_5(13).

Front

Solve for x: 5^{x-2}=13. Give the approximate answer to three decimal places.

Back

x \approx 3.594.

Front

What is the horizontal asymptote of the function y = 2^{x+2} + 1?

Back

The horizontal asymptote is y = 1.

Front

What transformations occur in the function y = 2^{x+2} + 1?

Back

The transformations are left 2 and up 1.

Front

Solve for x: 2e^{3x+4}-15=11. Give the exact answer.

Back

x = \frac{\ln{13}-4}{3}.

Front

What is the logarithmic property for \log\left(\frac{m^3}{n}\right)?

Back

\log\left(\frac{m^3}{n}\right) = 3\log{m} - \log{n}.

Front

What is the definition of a logarithm?

Back

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

Front

What is the change of base formula for logarithms?

Back

\log_b(a) = \frac{\log_k(a)}{\log_k(b)} for any base k.

Front

What is the relationship between exponential and logarithmic functions?

Back

If b^y = x, then log_b(x) = y.

Front

What is the natural logarithm?

Back

The natural logarithm is the logarithm to the base e, denoted as ln(x).