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 1012758: What is 3�10=(2�10)=(1�_)
Click here to see answer by fractalier(6550)

Question 1012884: good evening to all. Has somebody demo step by step why for
((0.12)^x)/((0.12)^(5-x))>0 all values of x are solutions?
Many thanks in advance!!
Click here to see answer by fractalier(6550)

Question 1012081: a) explain why a change in 'c' for the function 'a(b)^x-c + d' causes a horizontal translation.
b) explain why a change in 'd' for the function 'a(b)^x-c + d' causes a vertical translation.
Click here to see answer by fractalier(6550)

Question 1013157: Solve log(3x+1) - log(2x+3) = log 2 by graphing. Then solve the equation by using the Exponential - Logarithmic Properties. Explain the result.
Please include steps :D
Click here to see answer by fractalier(6550)

Question 1013165: For what values is log (2x+4)/(3x) defined? For what values is the logarithm positive?
Click here to see answer by josgarithmetic(39620)

Question 1013177: Simplify -x^2y^2/x^(1/2)y^0
Click here to see answer by fractalier(6550)

Question 1013655: similarity between the numbers 85,17,19,4 and 2.
Click here to see answer by Alan3354(69443)

Question 1013655: similarity between the numbers 85,17,19,4 and 2.
Click here to see answer by fractalier(6550)

Question 998702: Find the largest value of x that satisfies:
log(base2)(x^2)-log(base2)(x+4)=2
I was not able to find the answer, here are my step I tried to solve it.
log(base2)(x^2)-log(base2)(x+4)=2
log(base2) (x^2)/(x+4)=2
2^2= (x^2)/(x+4)
4= (x^2)/(x+4)
4(x+4)=x^2
4x+16=x^2
sqrt(4x+16)=x
2x+4=x
x=-4
Click here to see answer by Romolo(1)

Question 1013701: (√2^√2)^√2
Click here to see answer by Alan3354(69443)

Question 1014921: The spread of a virus can be modeled by exponential growth, but its growth is limited by the number of individuals that can be infected.� For such situations, the function
P(t)=Kpeřt/K+p(eřt-1)
can be used, where P(t) is the infected population t days after the first infection, p is the initial infected population, K is the total population that can be infected, and r is the rate the virus spreads, written as a decimal.
�
a)� A town of 10,000 people starts with 2 infected people and a virus growth rate of 20%.� When will the growth of the infected population start to level off, and how many people will be infected at that point?� Explain your reasoning, and include any graphs you draw with or without technology.

b)� When will the infected population equal the uninfected population?� Explain your steps.

Click here to see answer by Theo(13342)

Question 1015019: what is the interest rate to the nearest tenth of a percent of 20000=15000(1+r)^5?
Click here to see answer by LinnW(1048)

Question 1015102: Exponent and logarithm as functions of power
ln(2x)=3^-x+2
the key is x= 1.78
Click here to see answer by Alan3354(69443)

Question 1015402: Solve for x
2^x=-3
Click here to see answer by addingup(3677)

Question 1015402: Solve for x
2^x=-3
Click here to see answer by ikleyn(52800)

Question 1015407: Solve for x
log(base 4) x + log(base 4) (x-2) = 1
Click here to see answer by josmiceli(19441)

Question 1015407: Solve for x
log(base 4) x + log(base 4) (x-2) = 1
Click here to see answer by josgarithmetic(39620)

Question 1015407: Solve for x
log(base 4) x + log(base 4) (x-2) = 1
Click here to see answer by ikleyn(52800)

Question 1015404: Solve for x
log(x+6)-log(x)=log(15)
Click here to see answer by ikleyn(52800)

Question 1015406: Solve for x
6^(-x)=52
Click here to see answer by josgarithmetic(39620)

Question 1015405: Solve for x
3^(x)=log4
Click here to see answer by Alan3354(69443)

Question 1015518: solve for x
log (base 3) x + log (base 3) (x-2) = 1
Click here to see answer by Boreal(15235)

Question 1015518: solve for x
log (base 3) x + log (base 3) (x-2) = 1
Click here to see answer by MathTherapy(10552)

Question 1015517: solve for x
2*logx=20
Click here to see answer by Edwin McCravy(20059)

Question 1015525: How would you verify this equation?
5 - log3 + log1/2 = 5 - log6
Click here to see answer by Boreal(15235)

Question 1015512: Please help me solve this equation of translating an
exponential statement into an equivalent logarithmic one:
7^(1/2) = sqrt(7)
Click here to see answer by Edwin McCravy(20059)

Question 1015834: If u = log ( e^x + e^y ) , then ∂u/∂x + ∂u/∂y = ?
A ) e^x + e^y.
B ) e^x - e^y.
C ) 1/ (e^x +e^y).
D) 1
Click here to see answer by Fombitz(32388)

Question 1016245: Write the expression as a single natural logarithm:
3 IN x - 2 In c
Click here to see answer by Theo(13342)

Question 1016251: Hi,
I'm unsure on how to solve this problem:

Thank you so much to anyone who can help!
Click here to see answer by Alan3354(69443)

Question 1016251: Hi,
I'm unsure on how to solve this problem:

Thank you so much to anyone who can help!
Click here to see answer by ankor@dixie-net.com(22740)

Question 1016251: Hi,
I'm unsure on how to solve this problem:

Thank you so much to anyone who can help!
Click here to see answer by Theo(13342)

Question 1016259: Hello,
I came across this problem and I'm unsure how to solve it:

Thank you so much to anyone who helps.
Click here to see answer by Edwin McCravy(20059)

Question 1016259: Hello,
I came across this problem and I'm unsure how to solve it:

Thank you so much to anyone who helps.
Click here to see answer by macston(5194)

Question 1016368: Sketch a graph of the function by first making a tale of values
f(x)=x^2+2x=1
f(x)=square root x-2
f(x)/x+1/
Click here to see answer by Boreal(15235)

Question 1016461: solve for x and simplify:
log(base a) x + log (base a) (x+2)=2 where a>0, a does not equal 1
Click here to see answer by fractalier(6550)

Question 1016459: solve for x and simplify
3a^(2x) + 3a^(-2x) = 10 where a>0 and a cannot equal 1
Click here to see answer by Alan3354(69443)

Question 1016460: solve for x and simplify
4xln(1/4) - xln2= -6(x+1)ln(1/8)
Click here to see answer by ikleyn(52800)

Question 1016532: solve for x and simplify:
sqrte^(x-1)^2 < or = e^2
Click here to see answer by robertb(5830)

Question 1017039: 8log5 x^5 in a form that does not have exponents
Click here to see answer by ikleyn(52800)

Question 1017116: I reaally need help with this
~Joe deposits $1,500 in an account that pays 3% annual interest compounded continuously.
a.How much will Joe have in his account after 5 years?
b. How long will it take Joe to double his money?
Use natural logarithms and explain your answer.
Click here to see answer by rothauserc(4718)

Question 1017286: If x3 = 5, what is 1 more than x9?
Click here to see answer by macston(5194)

Question 1017556: please help me with (3^3x+1=9^2x-4
Click here to see answer by Fombitz(32388)

Question 1017860: 9^(-x)=27^(1-x)
Click here to see answer by Fombitz(32388)

Question 1017887: Solve: 2log5+logx-log5=2
Click here to see answer by fractalier(6550)

Question 1017911: A $10,500 investment has a 15% loss each year. Determine the value of the investment after
each of the following.
a. 1yr b.2yr c.4yr d.10yr
Click here to see answer by Cromlix(4381)

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