Here are three problems. (x-1)³-4 = 24 5^(x-1)-4 = 24

Let f x log3 x 3 and g x log3 x 1 Part A If h x f x g x solve for h x in simplest form 4 points 4 Part B Determine the solution to the system of nonlinear equations 6 points

Select the correct answer from each drop down menu Tests show that the hydrogen ion concentration of a sample of apple juice is 0 0003 and that of ammonia is 1 3 x 10 9 Find the approximate pH of each liquid using the formula PH log H where H is the hydrogen ion concentration The pH value of the apple juice is The pH value of ammonia is J S O 54 V 21

The rabbit population of Springfield Ohio was 144 000 in 2016 It is expected to decrease by 7 2 per ye Write an exponential function and use it to predict the rabbit population of Springfield in 2036 Rabbit population of Springfield in 2036 Round answer to the nearest whole number

Is x 0 a valid potential solution to the equation log x 2 log x 5 1 You don t need to solve this equation just determine if x 0 is a valid solution It can t be determined from the information given Yes since log 2 and log 5 both exist as valid values for the logarithm No because the logarithm of a negative value is undefined No because log 0 is undefined

A student was asked to determine the y intercept for the logarithmic function f x log3 x 2 1 Which of the following expressions would result in the correct y intercept log2 1 log3 log3 log2 1 3 1 2 1 2

Write the equation in exponential form. log9 81=2 The equation in exponential form is

Write the equation in logarithmic form. e¹=e The equation in logarithmic form is

Recall that the properties of logarithms also apply to the natural logarithms. a. Rewrite 3In(x)+4ln(2)-2ln(y) using a single natural logarithm. b. Rewrite In[(x - 3)(3x + 2)]³ in expanded form.

Anesthesia. When a person has a cavity filled, the dentist typically gives a local anesthetic. After leaving the dentist's office, one's mouth often is numb for several more hours. If 70 ml of anesthesia is injected into the local tissue at the time of the procedure (t = 0), and the amount of anesthesia still in the local tissue / hours after the initial injection is given by A 70e-05, how much is in the local tissue 4 hours later?

The initial bacterium count in a culture is 1200. A biologist later makes a sample count of bacteria in the culture and finds that the relative rate of growth is 15% per hour. a. Find a function that models the number of bacteria after t hours. [ n(t)=n_e"] b. What is the estimated count after 12 hours? c. After how many hours will the bacteria count reach 500,000?