Logarithms Questions and Answers

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

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. Assume that the variables represent positive real numbers. log2(p3/mn)=

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

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. Assume that the variables represent positive real numbers. 8 log6 x + log 6y =

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?

Suppose a sample of a certain substance decayed to 69.8% of its original amount after 300 days. (Round your answers to two decimal places.) (a) What is the half-life (in days) of this substance? days (b) How long would it take the sample to decay to one-third of its original amount? days

Warfarin is a drug used as an anticoagulant. After administration of the drug is stopped, the quantity remaining in a patient's body decreases at a rate proportional to the quantity remaining. Suppose that the half-life of warfarin in the body is 37 hours. Write a differential equation satisfied by Q: How many days does it take for the drug level in the body to be reduced to 35 percent of its original level? time =

Given f(x) = -log3 (x + 2) + 1, find the following. a. Use the transformations to find three points on the graph and the equation of the asymptote. b. Sketch the graph of f(x).

Here are three problems. (x-1)³-4 = 24 5^(x-1)-4 = 24 5^(x-1) — 4 = 24 Only one of these problems requires logarithms to solve. Which one? Explain why the other two problems do not require logarithms to solve. Please explain your justification with as much mathematical detail as possible.

Graph the function. h(x) = 6. (4/3)^x

Solve the following logarithmic equation. log (4x+6)= 1+ log (x - 5) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is {}. (Simplify your answer. Type an exact answer. Use a comma to separate answers as needed. B. There is no solution.

Use the properties of logarithms to write the expression as a single logarithm. Assume that all variables are defined in such a way that the variable expressions are positive. log9(x+5)+ log9(x+3) log9(x + 5) + log9(x+3)= ________

Solve for x: log6 (3x + 10) = 2 Write log6 (3x + 10) = 2 in exponential form. _________________ Find the value of x. x= ___________

e^(2x+1)=48 Write the equation as an equation involving logarithms. _______________ Find the solution of the equation in terms of logarithms, or correct to four decimal places. x=______________