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 1073488: write an equation for the graph of an exponential function with the points (0,0.5) and (2,14).
Click here to see answer by josgarithmetic(39620)

Question 1073555: what is (-1/4) to the 3rd power.
Click here to see answer by Fombitz(32388)

Question 1060027: A population of birds quadruples every 35 weeks.
A. Write a model for the number of birds in this population after x weeks.
B. Within 8 weeks, there were 300 birds. How many birds were initially present?
Click here to see answer by jorel1380(3719)

Question 1048706: How much time is needed for a sample of Pd-100 to lose 93.75% of its original amount? Pd-100 has a half-life of 3.634 days.Give an exponential model as a function t.
Click here to see answer by jorel1380(3719)

Question 1073704: I would like to know how to solve the equation (2 2/3 * 16 2/3) / 4 2/3
Thank you
Click here to see answer by ikleyn(52800)

Question 1073704: I would like to know how to solve the equation (2 2/3 * 16 2/3) / 4 2/3
Thank you
Click here to see answer by josgarithmetic(39620)

Question 1073695: for which values of m and n is
3logm-2logn the greatest
a)m=4. n=4
B)m=4. n=8
C)m=8. n=4
D)m=8. n=8
Click here to see answer by Fombitz(32388)

Question 1035108: between the start of 2005 and the end of 2009, the number of Facebook users can be modelled by the exponent equation u=0.43*(3.17)^t, where u is the number of users in millions nd t is the number of years since 2004 (1<=t<6)
How do I find the year in which the exponential model predicts that the number of users would first reach 200 million? (I know that the 1 year since 2004, the number of Facebook users is 1.4 million)
Thanks for your help
Click here to see answer by jorel1380(3719)

Question 1034815: On Monday, Lassister began monitoring the size of a bacteria colony. He noted that the mass of the colony grew from 5 grams at 8am to 6.5 grams at 2 PM.
a) find the value for k and write an exponential growth function that estimates the mass M of the bacteria colony t hours after 8 AM Monday.
b) What will the mass be at 6 PM Monday?
c) To the nearest hour, at what time will the mass of the growing colony reach 15 grams?
please explain.

Click here to see answer by jorel1380(3719)

Question 1073844: I need help reducing the equation:
log(base 2)((2(squareroot(3))/(5p))
So far I have:
log(base 2)(2(squareroot(3))-log(base 2)5p
Click here to see answer by josgarithmetic(39620)

Question 1073845: 4^(x-1)=3^2x
Click here to see answer by josgarithmetic(39620)

Question 1073846: log(base 5)(x-2)+log(base 5)(x+2)=1
Click here to see answer by josgarithmetic(39620)

Question 1073846: log(base 5)(x-2)+log(base 5)(x+2)=1
Click here to see answer by MathTherapy(10552)

Question 1018048: you saved $25000 to buy a new car in time for graduation in 2020. in 2010 you invested in a certain amount of your savings in a blue chip stock that yields 5% interest compounded monthly. find out much money you started with before you saved enough to buy a new car.
Please help. Thank you
Click here to see answer by jorel1380(3719)

Question 1074411: the number of rabbits in a certain population doubles every month and there are 20 rabbits present initially. Express the number of rabbits as a function of time.
Click here to see answer by Theo(13342)

Question 1074814: Solving exponential and logarithmic equations.
Solve the equation. Then check for extraneous solutions. 2(3)exponent 2x = 5
Click here to see answer by Boreal(15235)

Question 1074812: Properties of Logarithms. Condense the expression. 2 ln 3 - ln 5
Click here to see answer by Boreal(15235)

Question 1074819: use log_(5)2=0.4307 and log_(5)3= 0.6826 to approximate the value of log_(5)54
thank you
Click here to see answer by Boreal(15235)

Question 1074819: use log_(5)2=0.4307 and log_(5)3= 0.6826 to approximate the value of log_(5)54
thank you
Click here to see answer by MathTherapy(10552)

Question 1074826: solve 2log_(2)5x-log_(2)(x+1)=lne^(x)
Thanks
Click here to see answer by Alan3354(69443)

Question 1074826: solve 2log_(2)5x-log_(2)(x+1)=lne^(x)
Thanks
Click here to see answer by josgarithmetic(39620)

Question 1074807: Properties of Logarithms Expand the expression. ln 7x/3

Click here to see answer by josgarithmetic(39620)

Question 1074625: Find all positive integers $n$ for which $n^2 - 19n + 99$ is a perfect square.
Click here to see answer by KMST(5328)

Question 1074950: 1/8x=9
Click here to see answer by Alan3354(69443)

Question 1074820: 5log_(5)2x-log_(5)(x-3)=lne^(x+4)
Thank you
Click here to see answer by Alan3354(69443)

Question 1059123: Log2(3x+1) + log8(x-1)^3 =6
Click here to see answer by MathTherapy(10552)

Question 1032706: Log(5) - log (x) + log5 =(1/10) log 45
Click here to see answer by MathTherapy(10552)

Question 1018050: you saved $25000 to buy a new car in time for graduation in 2020. in 2010 you invested in a certain amount of your savings in a blue chip stock that yields 5% interest compounded monthly. find out much money you started with before you saved enough to buy a new car.
Please help.
Thank you
Click here to see answer by MathTherapy(10552)

Question 1075341: The exponential model A=824.4e^0.016t describes the population, A, of a country in millions, t years after 2003. Use the model to determine the population of the country in 2003.
Click here to see answer by Lightning_Fast(78)

Question 1075768: Let $Q(x) = x^2+bx+c$, where $b$ and $c$ are integers.
If $Q\left((1+\sqrt 2)^8)=0$, determine $b+c$.
Click here to see answer by ikleyn(52800)

Question 1075887: Does the following situation represent a linear or exponential model? Write a function to model the situation.
A painting is worth $400 and is increasing in value at 5% per year.
What is the value of the painting in 6 years?
Linear or Exponential?
Value:
Click here to see answer by ankor@dixie-net.com(22740)

Question 1075888: Does the table of values represent a linear or exponential model?
Write a function to model the situation
X 0 1 2 3 4 5 6
Y 4 7 10 13 16 19 22

Predict the value of y when x = 15
Linear or Exponential?
When x = 15, y =
Click here to see answer by josgarithmetic(39620)

Question 1075883: A certain bacterial culture triples every hour. After 5 hours there are about 8,000 bacteria in this culture. How many bacteria were there before the 5 hours passed? Write a function to model this situation and solve. Round to the nearest whole number.

Click here to see answer by josgarithmetic(39620)

Question 1075884: Posie�s plush puppy collection is now 24. Her collection is growing at a rate of about 50% per year. Copy and complete the table to predict the population for the next 5 years. Round to the appropriate place value.

Years 0 1 2 3 4 5
Population 24
Write a model. Graph the model on your calculator and find how long it will take to reach 1384 puppies? Round to the nearest tenth.
Click here to see answer by jorel1380(3719)

Question 1075882: The half-life of ibuprofen is about 1.8 hours. Here is the function to model the amount of ibuprofen remaining after t hours. The amount of ibuprofen taken is a.
y\:=\:a\left(0.5\right)^{\frac{t}{1.8}}
If 800mg are taken, how many milligrams remain in your system after 6 hours? Round to the nearest tenth.
Click here to see answer by jorel1380(3719)

Question 1075881: A ball is dropped from a height of 15 feet. The height of each bounce is 25% less than the previous bounce. What is the height of the ball after 12 bounces? Round to the nearest tenth.
Click here to see answer by jorel1380(3719)

Question 1075880: A cell phone depreciates in value by 20% every year. If the initial cost of the phone is $250, what is the value of the phone after 6 years? Write the function to model this situation and solve.

Click here to see answer by jorel1380(3719)

Question 1075886: Does the following situation represent a linear or exponential model? Write a function to model the situation.
Cooper has $75 in savings and is adding $15 each week.
How much will he have in 16 weeks?
Linear or Exponential?
After 16 weeks
Click here to see answer by jorel1380(3719)

Question 1075889: Does the table of values represent a linear or exponential model?
Write a function to model the situation.
X 0 1 2 3 4 5 6
Y 4 12 36 108 324 972 2916

Find the value of y when x = 12
Linear or Exponential?
When x = 12, y =
Click here to see answer by MathLover1(20850)

Question 1076971: Simplify the expression
https://ibb.co/dc9WY5
( use the link to see the problem please show work and thanks for the help also on the top row the numbers under log are all 3)
Click here to see answer by MathLover1(20850)

Question 1077171: 2log base 2 (x-6)- log base 2(4)=4
Click here to see answer by Boreal(15235)

Question 1077308: Solve e9x = 9.9 for x correct to four decimal places.

Click here to see answer by jorel1380(3719)

Question 1077653: solve 3^81^x = 81^3^x for x
(write answer in simplified form)
Click here to see answer by Alan3354(69443)

Question 1077518: solve 3^81^x = 81^3^x
(write the answer in simplest form)
thanks for the help
Click here to see answer by Alan3354(69443)

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