Questions on Algebra: Logarithm answered by real tutors!

Tutors Answer Your Questions about logarithm (FREE)

Question 149641: Please help with step by step to solve this equation.
log (x^(2)-15) = 1
Thank you.
Click here to see answer by vleith(2825)

Question 149625: Could I please get help with the following problem:
Find a general formula for the arithmetic sequence whose 8th term is -20 and the 17th term is -47
Thank You
Click here to see answer by nerdybill(6961)

Question 149739: evaluating a logarithm log 0.0837
Click here to see answer by stanbon(57361)

Question 149753: log x + log 2 = 5
Click here to see answer by jim_thompson5910(28595)

Question 149752: log r - log t + 2 log s
Click here to see answer by jim_thompson5910(28595)

Question 149755: 1. Find the value of the expression 1.05^9
2. Find number corresponding to the give logarithms - 8.05733-10
Click here to see answer by Alan3354(30993)

Question 149929: Exponential and Logarithmic Functions
Like always reading and translating these are tough. Thank you for helping
Problem: The level of a prescription drug in the human body over time can be found using the formula:
where D is the amount taken every n hours and H is the drug’s half-life in hours.
1.If 2.5 milligrams of Lorazepam with a half-life of 14 hours is taken every 24 hours, then to what level does the drug build up over time?
2.If a doctor wants the level of Lorazepam to build up to a level of 5.58 milligrams in a patient taking 2.5 milligram doses, then how often should the doses be taken?
3.What is the difference between taking 2.5 milligrams of Lorazepam every 12 hours and taking 5 milligrams every 24 hours?
4. What mathematical concepts are applyied and explain the steps in order to solve this problem
Thank you

Click here to see answer by stanbon(57361)

Question 149931: I have a question in regards to a problem that was already submitted and solved. THe question number is 149823, and it was solved by, vleith(790). THe question i have is around the second problem. I am having trouble understanding how we got the equation or answer of (1-(0.5)^n/14)= 2.5/5.58, and the next step says -(0.5)^n/14 = -0.552. How did we get - 0.552? and i am hoping this will help me understand the rest of the this problem. but if there is anyway of explaining the following steps to solve for this would be helpful.

Click here to see answer by jim_thompson5910(28595)

Question 149947: how to solve a logarithm problem?

Click here to see answer by Alan3354(30993)

Question 149960: 3 = e 0.05x
Click here to see answer by jim_thompson5910(28595)

Question 149961: 2 log base 3 9x= 8
Click here to see answer by jim_thompson5910(28595)

Question 149962: x
3(2 )=42
Click here to see answer by jim_thompson5910(28595)

Question 149967: what is the complete solution of logb2m-logbX^3..... hope u understand the equation...
Click here to see answer by stanbon(57361)

Question 149866: How do I complete this problem? For the exponential function ex and logarithmic function log x, graphically show the effect if x is doubled.
How do I calculate and plot these?
1. ex and e2x
2 logx and log2x
Correct reasoning of the effect of doubling the value of x in logarithmic and exponential functions
This is one tough question. Thanks so much.
Click here to see answer by josmiceli(9684)

Question 149976: These problems are really giving me some trouble, will someone please help!
If:
tanA=(-2/3) and 90 degrees < A < 180 degrees, find sinA.
Thank you again for your time, Natalie
Click here to see answer by stanbon(57361)

Question 149979: Please help, I don't even know where to start with this problem!
Which of the following describes the steps involved in using the graph of y=3 cos x + 3
1. Stretch the graph vertically by a factor of 3 and shift it to the left 3 units.
2. Stretch the graph vertically by a factor of 3 and shift it down 3 units.
3. Stretch the graph vertically by a factor of 3 and shift it to the right 3 units.
4. Stretch the graph vertically by a factor of 3 and shift it up 3 units.
Thank you again, this means so much, Natalie
Click here to see answer by oscargut(891)

Question 149971: Will someone please help me write this as a single logarithm!
1/2 ln (x^2 +1) -4 ln (1/2) -1/2[ln(x-4)+ln x]
Thank you so much, Natalie
Click here to see answer by oscargut(891)

Question 149981: Will someone please help me with the process on finding the real zeros of:
3x^4 + 3x^3 - 17x^2 + x - 6 = 0.
Thanx
Click here to see answer by Fombitz(13828)

Question 149980: Please help me!
If:
f(x) = 4-x and g(x) = 1+x^2 find (g*f)(-2)
Thanx
Click here to see answer by Fombitz(13828)

Question 149982: Find y as a function of x; the constant C is a positive number.
ln(y-1) + ln(y+1) = -x + C
Please help me with this; thanx
Click here to see answer by ankor@dixie-net.com(15656)

Question 150011: 5^x = 125 (find the exact answer and round 3 decimal points)
5^x = 15 (find the exact answer and round 3 decimal points)
Click here to see answer by Alan3354(30993)

Question 150019: solve for x.
2 log2 x - log2 (x+4)= log2 2
Click here to see answer by stanbon(57361)

Question 150019: solve for x.
2 log2 x - log2 (x+4)= log2 2
Click here to see answer by Fombitz(13828)

Question 150015: How long will it take for an investment to double in value if it is invested at 5% per annum compounded monthly?
Click here to see answer by scott8148(6628)

Question 150160: Could I please get some help with the following problem:
Find the sum:
9
∑ (-2k+8)
k=1
Thanks,
Ray
Click here to see answer by Fombitz(13828)

Question 150163: Could I please get some help with the following problem:
Find the sum:
10
∑
k=1
Thank You,
Ray
Click here to see answer by Fombitz(13828)

Question 150355: solve the following for x: 400/1+e^2^x = 100
Click here to see answer by Fombitz(13828)

Question 150311: Could I please get some help with the following problem:
Find the focus and the directrix of the parabola
Thank You,
Ray
Click here to see answer by checkley77(12569)

Question 150412: Express in terms of sums and differences of logarithms
logₐ x^3y^2z (after the log is a)
Can anyone help me solve this?

Click here to see answer by jim_thompson5910(28595)

Question 150439: Ok, here is a real life equation that I need to solve for a calulation I'm doing at work. I need to solve for x in the following equation:
A = B * (1+i)^x + C * (1+j)^x
where i and j are interest rates and A, B and C are dollar amounts. In story problem language the problem is: How long will it take for Fund B and Fund C combined take to grow to amount A given that Fund B is growing at i% and Fund C is growing at j%? I know I can't just multiply both sides by ln in this equation and have it work, so I'm not sure what to do with it.
Click here to see answer by stanbon(57361)

Question 150694: Hello E-Instructors :)

Would someone kindly show me how to solve this problem correctly?

Problem: The level of a prescription drug in the human body over time can be found using the formula:
L= ___D___
''''''''1-(1/2)^n/H
where D is the amount taken every 'n' hours and H is the drug's half-life in hours.
(''''These marks are merely spacers and not intended to be part of the equation).

1. If 2.5 milligrams of Lorazepam with a half-life of 14 hours is taken
every 24 hours, then to what level does the drug build up over time?

So far I think that the formula may look like this:
2.5 = ___24________
'''''''''''''1-(1/2)^24/14

Then maybe this:
2.5 = ___24____
'''''''''''''0.3047534

2.5 = 69.057991

Then, I don't know what to do next or if what I've done is even close to being right. :P

2. If a doctor wants the level of Lorazepam to build up to a level
of 5.58 milligrams in a patient taking 2.5 milligram doses, then how
often should the doses be taken?

I'm completely in the dark about this one.

3. What is the difference between taking 2.5 milligram of Lorazepam
every 12 hours and taking 5 milligrams every 24 hours?

This one, I might subtract results from these two equations:

2.5 = ___12_________
''''''''''''1-(1/2)^12/14
from
5 = ___24_______
''''''''''1-(1/2)^24/14

Well, that would be after I have learned how to solve the first question
correctly. ;)

Thank you so much for sharing your valuable knowledge with a mathematically challenged damsel like myself.
Grateful,
J. ;)
Click here to see answer by edjones(7569)

Question 150788: 23/15 (logBASE5 N+logBASE5 (n+11)) -12/13 logBASE5(n-10) Condense to the logarithm of a single quantity.
Click here to see answer by Fombitz(13828)

Question 150847: How can I rewrite this problem as a single logarithm: 7lnx + 4lny -3lnz
Click here to see answer by vleith(2825)

Question 150943: How do you graph f(x)=2^x and g(x)=log(base)2^x on the TI-83 calculator? Or the inverse of f(x)=2^x on the TI-83 calculator?
Thank you for you time.
Click here to see answer by jim_thompson5910(28595)

Question 150970: SOLVE THE EQUATION 3 x 5^(2t-1)=75
Click here to see answer by jim_thompson5910(28595)

Question 151008: Hi I do not have a calculator, I need a table of x and y (up to 9)values to plot a graph y = log2x Please help me.
Click here to see answer by mducky2(62)

Question 150966: For the exponential function ex and logarithmic function log x, graphically show the effect if x is doubled.
Click here to see answer by ankor@dixie-net.com(15656)

Question 151168: ln(5x-2)=12
Click here to see answer by nabla(475)

Question 151178: Story problem: A can of soda at 79 degrees F is placed in a refrigerator that maintains a constant temperature of 36 degrees F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by T(t)=36+43e^-.058t.
Part a) Find the temperature to the nearest degree of the soda 10 minutes after it is placed in the refrigerator.
I substituted 10 into the equation and got 60 degrees F. I understand this part.
Part b) When, to the nearest minute, will the temperature of the soda be 45 degrees F? HELP! I think that you need to plug in equations to graph it but I don't know what to plug in.
Thanks,
Rose
Click here to see answer by vleith(2825)

Question 151233: Please help. These log word problems are the worst.
A certain radioactive isotope decays at a rate of .25% annually. Determine the half-life of this isotope, to the nearest year.
Click here to see answer by ankor@dixie-net.com(15656)

Question 151243: In the formula A=I^ekt, A is the amount of radioactive material remaining from an initial amount I at a given time t and k is a negative constant determined by the nature of the material. An artificat is discovered at a certain site. If it has 53% of the carbon of the carbon-14 it originally contained, what is the approximate age of the artificat? (carbon-14 decays at the rate of 0.0125% annually.) Round to the nearest year.
Click here to see answer by stanbon(57361)

Question 151244: Suppose the amount of a radioactive element remaining in a sample of 100 milligrams after x years can be described by A(x)=100e^-0.01657x. How much is remaining after 257 years. Round the answer to the nearest hundredth of a milligram.
Click here to see answer by stanbon(57361)

Question 151242: If an earthquake measured 5.9 on the Richter scale, what was the intensity of the earthquake? Use the formula M=log(A/Ao).
Click here to see answer by stanbon(57361)

Question 151169: 2logx-log7=log112
Click here to see answer by Earlsdon(6287)

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, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890