91Ó°ÊÓ

In your own words, describe the characteristics of the graph of an exponential function. Use the exponential function defined by \(f(x)=3^{x}\) (Exercise 5 ) and the words asymptote, domain, and range in your explanation.

Use the indicated rule of logarithms to complete each equation. \(\log _{3} 3^{9}=\) _______ (special property)

Without using a calculator, give the value of \(\log 10^{31.6}\).

In Exercises 5–8, choose the correct response from the given list. Concept Check If a function is made up of ordered pairs in such a way that the same \(y\) -value appears in a correspondence with two different \(x\) -values, then A. the function is one-to-one B. the function is not one-to-one C. its graph does not pass the vertical line test D. it has an inverse function associated with it.

Which equation defines a one-to-one function? Explain why the others are not, using specific examples. A. \(f(x)=x\) B. \(f(x)=x^{2}\) C. \(f(x)=|x|\) D. \(f(x)=-x^{2}+2 x-1\)

Without using a calculator, give the value of \(\ln e^{\sqrt{3}}\)

Find each logarithm. Give approximations to four decimal places. \(\log 43\)

Use the properties of logarithms to express each logarithm as a sum or difference of logarithms, or as a single number if possible. Assume that all variables represent positive real numbers. $$ \log _{7}(4 \cdot 5) $$

Use the properties of logarithms to express each logarithm as a sum or difference of logarithms, or as a single number if possible. Assume that all variables represent positive real numbers. $$ \log _{8}(9 \cdot 11) $$

Find each logarithm. Give approximations to four decimal places. \(\log 98\)