Questions on Algebra: Exponent and logarithm as functions of power answered by real tutors!

Tutors Answer Your Questions about Exponential-and-logarithmic-functions (FREE)

Question 998835: Are the following statement true or false?
1)log(a,(b^4)) =(log(a,(^b)))^4
2)ln5sqrt(xy)=-5(lnx+lny)
3)lne^3=ln^5-lne^2
4)ln((3^b)(a^b))=b(lna+ln3)
I have answered these and one of them are wrong, I am not sure which one I got wrong.
1)False
2)True
3)False
4)False
Click here to see answer by MathLover1(20850)

Question 998888: Please help and show all steps. Thanks.

The population of foxes in the same forest is modeled by the formula:
P=400+(50)In(90t+1).

D) When the population of foxes is equal to 5% of the population of rabbits, the system is considered to be out of ecological balance. In how many years will the system be out of balance? my answer was 12.5years''.
Click here to see answer by josgarithmetic(39620)

Question 998886: Please help and show all the steps.
The function C(t)=5t/0.01t^2+3.3 describes the concentration of a drug in the blood stream over time when take orally. C is measured in micrograms per milliliter and t is measured in minutes.
A). Sketch a graph of the function over the first two hours after the dose is given. Label the axes.

B). Determine when the maximum amount of the drug is in the body and the concentration at that time.

C). Explain within the context of the problem the shape of the graph between taking the drug orally(t=0)and the maximum point. What does the shape of the graph tell us happens between the maximum point and two hours after taking the drug?

D.) Does this function have any asymptotes? If so, where are they? What do the asymptotes tell us about the concentration of a drug in our blood stream?
Click here to see answer by KMST(5328)

Question 998940: The equation (8x^8)(e^-6)-(3x^9)(e^-6)=0 has two roots.
Click here to see answer by MathLover1(20850)

Question 998833: The equation 8x^8e-6x-3x^9e^-6=0 has two roots.
I don't know how to solve this, I tried using the quadratic formula but it was not the right answer.

Click here to see answer by Fombitz(32388)

Question 999664: My question is 0=0.8(�)^x/1.3e9
I've tried rearranging it to give me log 0.8 + x/1.3e9 log(�)=0
But I still don't know how to solve for x
Click here to see answer by Fombitz(32388)

Question 1000090: In(x^2-1)
Click here to see answer by Alan3354(69443)

Question 1000408: 9^(2z)=102
Find z
Thanks
Click here to see answer by stanbon(75887)

Question 1000407: log_6 (204) = -4 t
Find t
Thanks
Click here to see answer by stanbon(75887)

Question 1000525: Find the exponential function of the given form that contains the given points.
Form: f(x)= c*(a^x)
Points: (0,4) and (4, 324)
I know the answer is f(x)=4*3^x,
Please explain, thanks!
Click here to see answer by solver91311(24713)

Question 1000716: 8^(x+3)=9^x
x=52.965 but please explain how to get there.
Click here to see answer by fractalier(6550)

Question 1000716: 8^(x+3)=9^x
x=52.965 but please explain how to get there.
Click here to see answer by MathLover1(20850)

Question 1000717: e^(x)+e^(-x)=3
x=0.9624 and -0.9624 but please explain how to get there.
Thanks
Click here to see answer by fractalier(6550)

Question 1000717: e^(x)+e^(-x)=3
x=0.9624 and -0.9624 but please explain how to get there.
Thanks
Click here to see answer by Alan3354(69443)

Question 1000771: Find the exponential function of the form f(x)=ae^(bx) that passes through the points (0,2) and (6,8)
I know the answer is f(x)=2e[(ln4)/6]x
but how do you get that?
Thanks
Click here to see answer by Fombitz(32388)

Question 1001180: The half-life of aspirin in your bloodstream is 12 hours.
How long will it take for the aspirin to decay to 70% of the original dosage?
Click here to see answer by Cromlix(4381)

Question 1001217: log(x+3)-log(x-2)=4log2
Click here to see answer by stanbon(75887)

Question 1001257: Solve the following equations:

Click here to see answer by fractalier(6550)

Question 1001258: Solve the following equation:

Click here to see answer by ikleyn(52800)

Question 1001259: Solve the following equations:

Click here to see answer by MathLover1(20850)

Question 1001259: Solve the following equations:

Click here to see answer by ikleyn(52800)

Question 1001348: Given x+1/x=7. Determine the values for x^2+1/x^2 and x^3+1/x^3 .
Click here to see answer by ikleyn(52800)

Question 1001940: Factor the common factor out of the expression. Please show work.
-24x^6-4x^4 +12x^3 +4x^2
Click here to see answer by Edwin McCravy(20059)

Question 1002178: 5.The Mendes family bought a new house 8 years ago for $129,000. The house is now worth $186,000. Assuming a steady rate of growth, what was the yearly rate of appreciation? Round your answer to the nearest tenth of a percent (1.2% etc)

Click here to see answer by stanbon(75887)

Question 1002177: 4.The annual Gross Domestic Product (GDP) of a country is the value of all of the goods and services produced in the country during a year. During the period 1985-1999, the Gross Domestic Product of the United States grew about 3.2% per year, measured in 1996 dollars. In 1985, the GDP was $577 billion. I what year did/or will the GDP equal $2.8 trillion?
Click here to see answer by josmiceli(19441)

Question 1002176: 3.An anthropologist finds bone that her instruments measure it as 0.824% of the amount of Carbon-14 the bones would have contained when the person was alive. How long ago did the person die?
The half life of carbon 14 is 5,730 years. Round your answer to the nearest thousand.

Click here to see answer by fractalier(6550)

Question 1002175: 2. An anthropologist finds bone that her instruments measure it as 0.146% of the amount of Carbon-14 the bones would have contained when the person was alive. How long ago did the person die?
The half life of carbon 14 is 5,730 years. Round your answer to the nearest thousand.

Click here to see answer by fractalier(6550)

Question 1002171: A radio active isotope decays according to the exponential decay equation where t is in days.
Round to the thousandths place.
For the half life: The half life is the solution (t) of the equation : a2=ae^−6.345t

Click here to see answer by Cromlix(4381)

Question 1002683: 2.A pool company forgets to bring their logarithmic charts, but they need to raise the amount of hydronium ions in a pool by 0.50. Using complete sentences, explain how your graph can be used to solve 10�y = 0.50. Find the approximate solution.
Click here to see answer by stanbon(75887)

Question 1002845: x+1/x

Click here to see answer by Fombitz(32388)

Question 1002959: Solve and check for extraneous solutions
(3x-5)^(1/2)=x-1
Click here to see answer by Alan3354(69443)

Question 1002959: Solve and check for extraneous solutions
(3x-5)^(1/2)=x-1
Click here to see answer by josgarithmetic(39620)

Question 1003151: What is the solution for 2 to the power 100
Click here to see answer by Edwin McCravy(20059)

Question 1003964: Write the following equation in its equivalent exponential form log5 25 = x
The I came up with is 25=5^x.
Is this correct?
Click here to see answer by rothauserc(4718)

Question 1004103: How long will a storm last that is 7 miles wide using this formula: t^2=d^3/216
Click here to see answer by MathLover1(20850)

Question 1004547: Good morning can you explain me why : 2^log2(x) = 8 gives as result x = 8 ??
Many Thanks
Click here to see answer by Theo(13342)

Question 1004632: How do you evaluate log27(1/3)?

Click here to see answer by fractalier(6550)

Question 1004881: Hello. I am trying to solve this exponential function but am not successful. Can you help me with it?
The equation is:
(1/3)^x+1=1/729 I know I need to find similar bases but how do I do that with this equation?
Click here to see answer by ikleyn(52800)

Question 1004990: If log(base 3)5=1.465 and log(base 3) 2=0.6309, what is the aproximate value of log(base 3)30?
Click here to see answer by stanbon(75887)

Question 1005050: Express as a single logarithm
4(ln(x)-2ln(y^3))+ln(z)
Click here to see answer by jim_thompson5910(35256)

Question 1005108: 2Log5^x + Log5^3
Click here to see answer by fractalier(6550)

Question 1005049: Express in terms of sums and differences of logarithms
log(sqrt6m^10n)

Click here to see answer by fractalier(6550)

Question 1005046: Please help me solve ln(c^7/dg^3
Click here to see answer by fractalier(6550)

Question 1005140: How do I solve the following equation e^x-e^x�x=0 ?.
Click here to see answer by addingup(3677)

Question 1005171: Express in terms of sums and differences of logarithms
log(sqrt(6m^10)n)
Click here to see answer by MathLover1(20850)

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