V1024(V64)") 1. Express exponential rules only. as a single exponent with a base of 2. Show all detailed work including the use of

Q: A culture of bacteria originally numbers 500. After 2 hours there are 1,500 bacteria. Assuming…

A: Given Initially bacteria are 500 after 2 hours they are 1500

Q: How are the two equations 102=100102=100nn and [][]log10(100)=2log10⁡(100)=2 related?

A: We need to show relation between given equation.

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A: We have to find the following conditions according to the given information

Q: log5 6 is irrational

A: We can prove given result by contradiction method:

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Q: What exponential function will pass through both (0,6) and (1,3)?

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Q: 4. Use the properties of logarithms to expand the expression as a sum, differences, and/or cons…

A: The given expression is logbx5b6y7z164 We expand the expression as sum , difference of logarithm…

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A: The number of cases on March 31th = 2966. The number of cases on July 28th = 45,314. The number of…

Q: Express th equation in exponential form.

A: a). Given, lnx+1=2 The exponential form is, x+1=e2         ∵lnx=y⇒x=ey⇒x=e2-1

Q: 8. Use the laws of logarithms to expand In in terms of sums, differences, (cos x)(x +1) and…

A: Some properties of logarith m are :(i) ln(a b) = ln a + ln b(ii) lnab = ln a - lnb(iii) ln ab = b l…

Q: Use the definition of Exponential Notation to prove the Exponent Law that says: (x2)3 = x6

A: Please see the explanation below

Q: jlog(4- ji') (541.5) In log(4ejn) j log(-7)

A:

Q: V1024(V64)*) Express as a single exponent with a base of 2. Show all detailed work including the use…

A: Given:     To determine: Express the given expression as a single exponent of base 2.

Q: Use these formulas to express the numbers in Exercises 61–66 interms of natural logarithms.61.…

A:

Q: Find exponential equation by using these two point (-2,6) and (3,1)

A: Consider y=aebx for some real numbers a and b. As (-2,6) satisfies the equation,…

Q: 2. Express in terms of sums and differences of logarithms In 2 3x³y (In 2 divided by 3x³y)

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Q: Determine whether the statement makes sense or does not make sense, and explain your reasoning : "I…

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Q: Because of a virus introduced into a bacterial culture, the population of the bacteria decreased…

A: Exponential decay is N = 50000e-λt Therefore, 30000 at t= 54 min Therefore 30000 = 50000e-λ54…

Q: write as sum/difference of logathirims. express powers as factors.    log2 (xy^6 / z^2)…

A: Logarithm

Q: A culture of a certain bacterium grows according to the law of exponential growth. If there were 130…

A: 1. The exponential growth is given by the where N(t) is the no of insects at a time t .N0 is the…

Q: b). Condense the expression into the log of a single quantity: 3logx + 2logy - logz Ans.

A: Given, The expression 3log x + 2log y -12log z.

Q: Determine whether the following statement is true or false, and explain why. (ln 3)4 = 4 ln 3

A: We know that, ln an=n ln a ; n is an integer

Q: How long will it take for $4000 to double in value if it is deposited in an account bearing 7%…

A: Let the time taken be t years

Q: The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the…

A: we formulate the question with the help of formula  N =Noe-λt where No = initial mass N = remaining…

Q: .Express in index notation: a) loga 8 = c ii. Simplify: 3log3 - log 27

A: I.Express in index notation:  a) loga 8 = cAnswerlogam=n ⇒ m=anThereforeloga8 = c ⇒8=ac

Q: The half-life to exponential mod amount of

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Q: Between which two consecutive integers must log, (40) lie? Be sure to explain your reasoning. //…

A: We have the given number as log340 Let us consider that, 33<40<34

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Q: What is their doubling time?  By what factor will proces increase in 2years? in 9years?

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Q: Expand In 1 into a sum or difference of logarithms containing no exponents. Question Help: DPost to…

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Q: In 1990, a scientist found 751 g of a new isotope. After 5 years it had decayed to only 500 g. If…

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Q: A certain ball is dropped from a height of x feet. It always bounces up to 2/3x feet.  Suppose the…

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Q: A computer viruS can grow exponentially just like a real virus in a person's body. Suppose the…

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Q: use exponent laws to explain why 3 ln 2 is equivalent to ln8

A: By exponent law     mlna = lnam    for any a and m.

Q: 2log(base 2)(x-8)-log(base 2)x=2

A: Given,

Q: Find a real root of 3x – log10 x – 8 using the Successive Approximation method. Correct to four…

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Q: How are the two equations 102 = 100 and log10 100 = 2 related?

A: Here I am attaching image so that you understand each and every step.

Q: A computer loses 35% of of its value each year. If the computer cost $600 new, calculate its value…

A: A computer loses 35% of of its value each year. If the computer cost $600 new, calculate its value…

Q: express ln 3√4 in terms of ln 2 and/or ln 3

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Q: The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the…

A:

Q: 5. What term number contains x* in x' + identifying the exponential pattern on the variable x,…

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Q: A freshly inoculated bacterial culture of Streptococcus contains 100 cells. When the culture is…

A: General expression for exponential growth function is given by,                   n(t) = a(1+r)t…

Q: A computer virus can grow exponentially just like a real virus in a person's body. Suppose the…

A: Given that: Initial bytes infected = 11 bytesRate of growth = 7% per min.

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Q: The logarithm of a product of two numbers is the same as the--Select-- v of the logarithms of these…

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Q: Suppose that a population is 3000 at the beginning of 1980, and that it grows at 8% a year. What is…

A: Given:  Population is 3000 at the beginning of 1980, and that it grows at 8% a year.  To Find:…

Q: The count In a bacteria culture was 100 after 20 minutes and 1700 after 35 minutes. Assuming the…

A: