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 872759: How do I solve log 20= log (x-6) -log16
Click here to see answer by Alan3354(69443)

Question 872836: Solve the following equations for x:

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Question 872836: Solve the following equations for x:

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Question 872990:
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Question 873432: I need help learning how to do this problem:
A culture of bacteria doubles after 9 hours.
What proportion of the original number of bacteria
(Q sub 0)
will be present after 18 hours?
Thank you for any help on how to set it up!
Click here to see answer by jim_thompson5910(35256)

Question 873478: A population initially contains 1000 individuals. Each year, 4% of the population is lost, and 6% is gained, what is the size of the population after 7 years?
Click here to see answer by josgarithmetic(39620)

Question 873775: Write the equation of the line which passes through (3,0) and has the same slope as the line 2x - y=1
Click here to see answer by ewatrrr(24785)

Question 873772: Find the slope of the line given by the equation 2x + 4y +5=0
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Question 873884: Simplify -x^2y^2 / x^1/2y^0
Please show all of your work :)

Click here to see answer by rothauserc(4718)

Question 873890: If f(x) = 2x + 4, and g(x) = (x^2 + x + 5), find g(f(x))
Click here to see answer by Fombitz(32388)

Question 874104: y=2xlogx^2
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Question 874162: solve 2x^2+2x-8=3x-6
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Question 874178: 2logx+log5
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Question 874178: 2logx+log5
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Question 874625: Could someone show me the steps involved in solving this equation:
9^2x * (1/3)^(x+2) = 27 * (3^x)^-2
The book says that the answer is 1 but I get an answer of 1/5. I solve the problem all the way down to:
3^(3x+2) = 3^(3-2x) then I set the exponents equal to each other and solve for x: 3x + 2 = 3 - 2x and I get 1 for and answer. I can't figure out how they get 1 for an answer for x.
Could someone please help.
Thanks.
Click here to see answer by richwmiller(17219)

Question 874623: Could someone please show me the steps in solving this problem.
(e^7x - e^-7x)^2 - (e^7x + e^-7x)^2 / (e^7x + e^-7x)^2
The book says that the answer is -4 / (e^7x + e^-7x)^2
I don't know how they got -4 for the numerator. I am getting something completely different.
Thanks in advance.
Click here to see answer by mananth(16946)

Question 875193: how do you solve 16^(-1/4)
Click here to see answer by ewatrrr(24785)

Question 875557: Please help I have the equation:
(1/8)*2^(-3r) = 2^(-r)
I need to solve for r but i do do not know how since I have that "1/8" please help me understand why we do each step to solve the problem.
Click here to see answer by ewatrrr(24785)

Question 875776: Find the exact value of the logarithmic expression.
ln l
Click here to see answer by jim_thompson5910(35256)

Question 876044: the graph of f(x) contains the point (3,-4). What point must be on the graph of f(x) + 5
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Question 876133: how would you solve 10^3x=41
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Question 876171: how do you evaluate log base 3 sub 5, rounding to the nearest hundreth?
Click here to see answer by jim_thompson5910(35256)

Question 876346: I need to know how to do this problem, I've been stuck on it for awhile and I have to present it in front of the class tomorrow with the steps could you help me out? Find the asymptotoes F(x)= x^2+3x-4 over 2x^2-3x-2
Click here to see answer by ewatrrr(24785)

Question 876638: Find the equation of the tangent to the curve y= e^x +x which is perpendicular to the line 4y+x=0
Click here to see answer by Fombitz(32388)

Question 877115: How do you simplify 25^1/2 * 25^1/4 ??
Click here to see answer by josgarithmetic(39620)

Question 877066: Ln(x+1) - ln x=2
Click here to see answer by jim_thompson5910(35256)

Question 877068: Log(base 2) (x+1)-log(base 4) x=1
Click here to see answer by lwsshak3(11628)

Question 877319: Find the derivative of the following function: (x^2)^sin x.
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Question 877667: What is the exact value of x?
-e^(-x)+2e^(-2x)=0
Click here to see answer by josgarithmetic(39620)

Question 877321: Evaluate the following integrals using the given substitutions.
(a)(3x^2 + 10x)dx/(x^3 + 5x^2 + 18), substitution u = x^3 + 5x^2 + 18;
(b)(14x + 4) cos(7x^2 + 4x) dx, substitution u = 7x^2 + 4x.

Click here to see answer by Fombitz(32388)

Question 877781: Solve for x.
ln(2x+1)+6=13
Give your answer correct to four decimals.
Click here to see answer by Fombitz(32388)

Question 877781: Solve for x.
ln(2x+1)+6=13
Give your answer correct to four decimals.
Click here to see answer by cigany29(23)

Question 877773: Solve for x.
ln(x-1)=5
Give your answer correct to four decimals.
Click here to see answer by Fombitz(32388)

Question 877838: How do you solve: e^(In x)= 1
Thanks!
Click here to see answer by Alan3354(69443)

Question 877902: Write an exponential function of the form y = ab^x that includes he given points. (1,2) and (4,128)
Click here to see answer by jim_thompson5910(35256)

Question 877963: What is the value of x?
ln(x)*x^(1/2)=0
Click here to see answer by jim_thompson5910(35256)

Question 878203: Simplify the expression.

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Question 878152: 6^9a < 15

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Question 878345: Please i would like some help with this log problem I've been trying to solve for hours.
log4+log25-3log2-3log5= ( condensing first)
Click here to see answer by Fombitz(32388)

Question 878353: i need help solving this two exponential and logarithmic equations i have tries solving them and need to verify my answers
a) 4^4x-5=8
b)5^2x-1=9
Click here to see answer by Fombitz(32388)

Question 878204: Solve the inequality.
log8(2x) > 2

Click here to see answer by lwsshak3(11628)

Question 878205: Solve the equation.

x:___,___
Click here to see answer by Fombitz(32388)

Question 878685: I need help in writing the expression as one logarithm:
2 log (Y^10/x) - 6 log y + 1/2 log (x^4*y^2)
Thank you!
Click here to see answer by lwsshak3(11628)

Question 878786: Could someone help with this problem:
Find the exact solution, and a two-decimal-place approximation of the solution, when appropriate:
4^(2x+3) = 5^(x-2)
The book says that the answer is -(ln 1600/ ln (16/5)) which is approximately -6.3
Could you show me the steps at how that answer was derived because I keep getting a different answer.
Thank you.
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