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 1117128: solve the system x^2+y^2=37, 3x-9=y there are two solutions: (x1,y1) and (x2,y2)
Evaluate x1+y1+x2+y2=
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Question 1115951: Find the indefinite integral
5.(4+ 1/X^2)(-2/x^3)dx
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Question 1117237: Integral 1/4 Sqrt((x^2/4)-1)^3
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Question 1117235: Integral of squareroot(x^2-4)^3 dx
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Question 1117433: -11+(-5)+(-2)
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Question 1118211: How is actually to state two consecutive integers that lie between the logarithms?
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Question 1118244: Compare 10^2 and 2^10. For any two numbers make a conjucture about which usually gives the greater number, as the base or as the exponent.
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Question 1118718: Population Growth: A population is increasing according to the exponential function
y=2e^0.02x
Where y is in millions and x is the number of years. Match each question in column I with the correct procedure in column II.
Column I - When will the population reach 3 million?
Column II answer options:
1. Evaluate y=2e^0.02(1/3
2. Solve 2e^0.02x=6
3. Evaluate y=2e^0.02(3)
4. Solve 2e^0.02x=3

Click here to see answer by josgarithmetic(39620)

Question 1119205: Below is a list of elements and their known half-life. Using the given half life determine an exponential function that gives the proper decay rate for the given element. Create a table of values listing the amount of the element you started with and then determining the amount of time to go from 1,000 units to the amount in the table
Amount Remaining Years/Days to Decay to Remaining Amount 1000 900 800 700 600 500 (half life) 400 300 200 100 0

Make sure to show the work for each calculation as a function of time, A(t), where A is the amount remaining and t is time in years/days (depending on the half-life value.) You will be using a log function to calculate the time.

Make a graph of your table plotting out all points in the table. Use an appropriate scale for your graph and state the scale. Your axes should reflect the function A(t) (meaning one should be labeled A and the other t.)

Element/Isotope Half-Life Barium (Ba) 133 10.5 years
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Question 1119440: Solve 5^x=3^x+2
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Question 1119440: Solve 5^x=3^x+2
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Question 1119898: Let b > 0 and b ≠ 1. Express y = b^x in logarithmic form. Also state the domain and range of the logarithmic function.
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Question 1120054: The largest earthquake in the US occurred in Alaska on March 28, 1964. It registered a magnitude of 9.2. How much energy was released in this earthquake? In the blank below, fill-in the missing part of the answer.
The energy released was 1.58 x 10^??.
_____________________________________
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Question 1121359:
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Question 1122142: The growth of a certain species (in millions) since 1970 closely fits the following exponential function where t is the number of years since 1970.
A(t)=3500e^0.0166t
a. The population of the species was about 4142 million in 1980. How closely does the function approximate this value?
b. Use the function to approximate the population of the species in 2000. (The actual population in 2000 was about 5869 million)
c. Estimate the population of the species in the year 2015.
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Question 1122199:
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Question 1122243: Please help me convert a complex number to polar form and exponential form.
2+2(sqrt3i)
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Question 1122328: 4^x^2-3x=1/16
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Question 1122631:
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Question 1122720: Find all the positive integers k for which 7�(2^k)+ 1 is a perfect square.
I started by setting it to 7�(2^k)+1=x^2 where x^2 represents perfect squares. Then i rearranged to 7�(2^k)=x^2-1. Then I used difference of two squares to get 7�(2^k)=(x+1)(x-1). I then used logs to rearrange it for k, but I am not sure if that is right or if I am even on the right path.
Thank you for taking the time to attempt this in advance!!
Click here to see answer by ankor@dixie-net.com(22740)

Question 1122980: find x
log(x,(log(2,256)) = 3
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Question 1123489: f a rock is thrown upward on the planet Mars with a velocity of 16 m/s, its height (in meters) after t seconds is given by H = 16t − 1.86t2.
(a) Find the velocity of the rock after one second.
m/s
(b) Find the velocity of the rock when t = a.
m/s
(c) When will the rock hit the surface? (Round your answer to one decimal place.)
t = s
(d) With what velocity will the rock hit the surface?
m/s
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Question 1123656: pre calculus express as a sum ( log 1ooo to a power over b to the 2 power)
2. 2log A -5LOGc+3 LOG b express to single log
3. solve 4 to the x+ 1 power x 2= 16

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Question 1123538: What is the Big O of (n/2) log(n/2) + f(n), where f(n) = o (sqrt n log^9 n)?
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Question 1123802: Having difficulty solving this problem. I appreciate the help
The numbers of milligrams D(h) of a drug in a patient's bloodstream h hours after the drug is injected is modeled by the following function.
D(h)=25e^0.2h
Find the initial amount injected and the amount in the bloodstream after 6 hours.
Round your answer to the nearest hundredth if necessary.
Find:
Initial amount:
Amount after 6 hours:
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Question 1124995: Write an exponential function y = abx for a graph that includes (�3, 16) and (�1, 4)
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Question 1124994: Graph the exponential model . y=2(0.5)^x Which point lies on the graph?
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Question 1125021: Let�s combine our knowledge of solving systems and solving logarithmic equations. Solve the system of equations: log y x=3
and log y 4x=5
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Question 1125111: please help me solve {odd positive numbers less than 30}
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Question 1125313: Hpw many days will take 5000$ to get a) 100,000$ and b)250,000$ at the compunded interest rate of 1% per day.....
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Question 1125312: GENERAL: Hailstones A hailstone (a small sphere of ice) is forming in the clouds so that its radius is growing at the rate of 1 millimeter per minute. How fast is its volume growing at the moment when the radius is 2 millimeters? [Hint: The volume of a sphere of radius r is V = 4/3*pi r^3.]
Click here to see answer by Alan3354(69443)

Question 1125372: Evaluate f(0), f(1),and f(2). Round your answer to three decimal places.
A) Express e^(kt) in the form b^(t).
B) Express 1/e^(x) in the form b^(x).
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Question 1126170: Is the sequence a^n=6n-17 arithmetic?
if it is what is its first term
and its common difference ?
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Question 1126191: How many whole numbers are there, whose squares and cubes have the same number of digits?
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Question 1126191: How many whole numbers are there, whose squares and cubes have the same number of digits?
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Question 1126167: If the 100th term of an arithmetic sequence is 213, and its common difference is 2, then
its first term
a^1=
a^2=
a^3=
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Question 1126167: If the 100th term of an arithmetic sequence is 213, and its common difference is 2, then
its first term
a^1=
a^2=
a^3=
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Question 1126659: 6^2/x+4^1/x=10/3*12^1/x
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Question 1126742: Expand the Logarithmic expression as much as possible
log(^9sqrt(x/z))
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Question 1126744: Solve the equation algebraically. Obtain a numerical approximation for your solution and check it by substituting into the original equation.
3ln(x-3)+7=8
round to 3 decimal places
Thank You!!
Click here to see answer by josmiceli(19441)

Question 1126746: A cup of coffee has cooled from 92degreesC to 50degreesC after 13 minutes in a room at 24degreesC. How long will it take to cool to 30degreesC?
Thank you!
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Question 1126743: Graph the function below, and analyze it for domain, range, continuity, increasing or decreasing behavior, asymptotes, and end behavior.
f(x)=log7(49x)
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910