Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round the answer to three decimal places.

log$_\pi \sqrt{2}$

Between 12:00 PM and 1:00 PM, cars arrive at Citibank’s drive-thru at the rate of 6 cars per hour (0.1 car per minute). The following formula from probability can be used to determine the probability that a car will arrive within t minutes of 12:00 PM: $F(t)=1-e^{-0.1 t}.$ What value does F approach as t becomes unbounded in the positive direction?

Between 12:00 PM and 1:00 PM, cars arrive at Citibank’s drive-thru at the rate of 6 cars per hour (0.1 car per minute). The following formula from probability can be used to determine the probability that a car will arrive within t minutes of 12:00 PM: $F(t)=1-e^{-0.1 t}.$ Determine the probability that a car will arrive within 40 minutes of 12:00 PM (before 12:40 PM).

Between 12:00 PM and 1:00 PM, cars arrive at Citibank’s drive-thru at the rate of 6 cars per hour (0.1 car per minute). The following formula from probability can be used to determine the probability that a car will arrive within t minutes of 12:00 PM: $F(t)=1-e^{-0.1 t}.$ Determine the probability that a car will arrive within 10 minutes of 12:00 PM (that is, before 12:10 PM).

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places.

log$_{\pi}$ e

Use transformations to graph the function. Determine the domain, range, and vertical asymptote of the function. Verify your results using a graphing utility.

$$f(x)=3 \ln x$$

A model for the number N of people in a college community who have heard a certain rumor is $N=P\left(1-e^{-0.15 d}\right)$ where P is the total population of the community and d is the number of days that have elapsed since the rumor began. In a community of 1000 students, how many students will have heard the rumor after 3 days?

Use transformations to graph the function. Determine the domain, range, and vertical asymptote of the function. Verify your results using a graphing utility.

$$h(x)=\ln \left(\frac{1}{2} x\right)$$

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places.

log$_{\sqrt{5}}$ 8

Change the exponential statement to an equivalent statement involving a logarithm.

$$3.7=a^8$$

The equivalent logarithmic equation is ?.

Use transformations to graph the function. Determine the domain, range, and vertical asymptote of the function. Verify your results using a graphing utility.

$$g(x)=\ln (2 x)$$

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places.

log$_{\sqrt{2}}$ 7

The function $D(h)=5 e^{-0.4 h}$ can be used to find the number of milligrams D of a certain drug that is in a patient’s bloodstream h hours after the drug has been administered. How many milligrams will be present after 1 hour? After 6 hours?

The normal healing of wounds can be modeled by an exponential function. If $A_{0}$ represents the original area of the wound and if A equals the area of the wound, then the function $A(n)=A_{0} e^{-0.35 n}$ describes the area of a wound after n days following an injury when no infection is present to retard the healing. Suppose that a wound initially had an area of 100 square millimeters. How large will it be after 10 days?