91Ó°ÊÓ

In Exercises 73-78, (a) plot the points, (b) find the distance between the points, (c) find the midpoint of the line segment joining the points, and (d) find the slope of the line passing through the points. $$ (4,-3),(-6,1) $$

Condense the expression to the logarithm of a single quantity. $$ 4[\ln z+\ln (z+5)]-2 \ln (z-5) $$

\(f(x)=\log (x-1)\)

In Exercises 67-74, use a graphing utility to graph and solve the equation. Approximate the result to three decimal places. Verify your result algebraically. $$ e^{2.724 x}=29 $$

In Exercises 73-76, use properties of exponents to determine which functions (if any) are the same. $$ \begin{aligned} &f(x)=16\left(4^{-x}\right) \\ &g(x)=\left(\frac{1}{4}\right)^{x-2} \\ &h(x)=16\left(2^{-2 x}\right) \end{aligned} $$

In Exercises 75-102, solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$ \ln x=-3 $$

In Exercises 73-78, (a) plot the points, (b) find the distance between the points, (c) find the midpoint of the line segment joining the points, and (d) find the slope of the line passing through the points. $$ (3,3),(14,-2) $$

Condense the expression to the logarithm of a single quantity. $$ \frac{1}{3}\left[2 \ln (x+3)+\ln x-\ln \left(x^{2}-1\right)\right] $$

\(f(x)=\ln (x-1)\)

In Exercises 73-76, use properties of exponents to determine which functions (if any) are the same. $$ \begin{aligned} &f(x)=e^{-x}+3 \\ &g(x)=e^{3-x} \\ &h(x)=-e^{x-3} \end{aligned} $$