91Ó°ÊÓ

Fill in the blanks. The exponential function \(f(x)=e^{x}\) is called the___ ___ function, and the base \(e\) is called the ___.

In Exercises \(4-6,\) match the property of logarithms with its name. (a) Power Property (b) Quotient Property (c) Product Property $$\log _{a}(u v)=\log _{a} u+\log _{a} v$$

In Exercises \(4-6,\) match the property of logarithms with its name. (a) Power Property (b) Quotient Property (c) Product Property $$\ln u^{n}=n \ln u$$

Determine whether each \(x\) -value is a solution (or an approximate solution) of the equation. \(\log _{2}(x+3)=10\) (a) \(x=1021\) (b) \(x=17\) (c) \(x=10^{2}-3\)

(a) solve for \(P\) and (b) solve for \(t\) $$A=P e^{r t}$$

In Exercises \(4-6,\) match the property of logarithms with its name. (a) Power Property (b) Quotient Property (c) Product Property $$\log _{a} \frac{u}{v}=\log _{a} u-\log _{a} v$$

Determine whether each \(x\) -value is a solution (or an approximate solution) of the equation. \(\ln (2 x+3)=5.8\) (a) \(x=\frac{1}{2}(-3+\ln 5.8)\) (b) \(x=\frac{1}{2}\left(-3+e^{5.8}\right)\) (c) \(x \approx 163.650\)

(a) solve for \(P\) and (b) solve for \(t\) $$A=P\left(1+\frac{r}{n}\right)^{n t}$$

Fill in the blanks. The domain of the natural logarithmic function is the set of___________ ,_______.__ ,_________.

Exercises \(7-10\), rewrite the logarithm as a ratio of (a) common logarithms and (b) natural logarithms. $$\log _{5} 16$$