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 39439: I need this for work ASAP.
What is the derivative

I need this for work ASAP.
What is the derivative
d/dx( f(x) ^ g(x) )
where ^ is the sign of EXPONENTIATION and f and g are function of x.
Please NOTE AGAIN that I am not talking about a compound function, I am talking about one function taken TO THE DEGREE of another.
thanks
Click here to see answer by astromathman(21)

Question 39504: Hello! I need help on this one math problem. It seems complicated but I know that it is easier than it looks. Please, if you can , help me!!
Problem: Solve for x
Verify your result by checking that it approximately satisfies the original equation.
2^4x+5=17
log(2^4x+5)=log17
4x+5log2=log17
And that's where I stopped because I have NO IDEA what to do next!!
HELP MEEEEEEEEEEEE!!

Click here to see answer by AnlytcPhil(1278)

Question 39577: Multiply.
4xy^3*2x^2*5xy^2
Click here to see answer by AnlytcPhil(1278)

Question 39615: Write the answer without negative or zero exponents: a-3
Click here to see answer by AnlytcPhil(1278)

Question 39672: the volume of a sphere can be fiven by the formula V=4.18879rcubed. You have to design a spherical container that will hold a volume of 75 cubic inches. What should the radius be?
Click here to see answer by checkley71(8403)

Question 39666: I can not figure out for the life of me how to do this. I have tried so many times, please, HELP.
Solve:
3log(5x)+4log(2x)=3
log(125x^3)+log(16x^4)=3
Have I done it right so far? For some reason it seems wrong.Please help me!!
Click here to see answer by Earlsdon(6287)

Question 39671: The volume of a spehere can be given by the formula V=4.18879rcubed
Click here to see answer by fractalier(2101)

Question 39873: Hello Math Wizards! I have the answer to the ff: problems but I want to confirm that my answer is correct.
Find the center, vertices and foci of the ellipse given by each equation.Sketch the graph.
1. x^2/49 + y^2/36 =1
2. ( x + 3 )^2/9 + ( y - 2)^2/16 = 1
Thanks,
Jo

Click here to see answer by stanbon(57399)

Question 39980: I am supposed to write the following expression as one logarithm.
2logx+ 1/3log(x+2)-4log(x-3)
Click here to see answer by Nate(3500)

Question 40006: log(5)625+log(9)(x-3)=6 need help please
Click here to see answer by fractalier(2101)

Question 39984: log4(2x+3)-logx=3
Click here to see answer by fractalier(2101)

Question 40021: y=a^x
I forget how to even start this. Let alone complete this.
Click here to see answer by longjonsilver(2297)

Question 40052: Use the distributive property to remove the parentheses in the following expression. Then simplify your result if possible.
1/4 (20+16)
Click here to see answer by fractalier(2101)

Question 40039: Please help me with these three problems.
1. Find the solution to the equation log(x)8=1/3.
2. Find the approximate solution to the equation 3(1.5^x)+10=280.
3. Find the solution to the equation 2 log(a)3 + log(a)(x-4)= log(a)(x+8).
() below the log
Thank you very much.
Chris
Click here to see answer by fractalier(2101)

Question 40284:
Click here to see answer by mbarugel(146)

Question 40433: the direction is to simplify the expressions using the inverse relationship between logarithms and exponents
ll^log11x
ln^ex
e^lnx

Click here to see answer by stanbon(57399)

Question 40754: I desperately need help with these few questions. This is a take home test that needs to be done by tommorow.
1. The number of bacteria present in a culture is B=10e^1923t where t is the time in minutes. Find the time required, to the nearest half minute, to have 3200 bacteria present.
12. log(5x-1)=2+log(x-2)
13. log(x^3)=(logx)^2
Thank you Very Much,
Art
Click here to see answer by stanbon(57399)

Question 38872: i know its already solved but i need to know how to prove it
6log base 6^(3x-1)= (3x-1)
thanks a bunch!
Click here to see answer by DavidChandler(2)

Question 35346: If log8 (little 8)M= log5 (little 5)7/log5(little 5)8, then M = ?
Click here to see answer by DavidChandler(2)

Question 36187: how do you solve this problem : 2e and then in the exponent log base 3 (x +2) = 14?
Click here to see answer by astromathman(21)

Question 40816: 5^x=-3x+6 need help
Click here to see answer by stanbon(57399)

Question 40817: 3(1.3^x)=X^2-2
Click here to see answer by stanbon(57399)

Question 40824: how do you solve this system of equation:
x^2+y^2=36
x+y=4
Click here to see answer by fractalier(2101)

Question 40823: how do you solve this system of equation:
y=-2x^2+8x+27
2x+y=15
Click here to see answer by zeynep(43)

Question 41270: Hi I have been trying to figure out the steps in the equation of 4x+3=2x10^-4
I just need a little refresher if possible. this is a sample equation. Thanks!
Click here to see answer by psbhowmick(529)

Question 41304: Simplify: x not equal to 0.
Click here to see answer by zeynep(43)

Question 41306: Find Positive Root:
Click here to see answer by Earlsdon(6287)

Question 41300: I am getting stuck on this one:
1/8=4^5x-2
Please Help
Click here to see answer by psbhowmick(529)

Question 41370: If log (base of 3) 8=1.8928 and log (base of 3) 2=0.6309, what is the value of log (base of 3) 16?
Click here to see answer by venugopalramana(3286)

Question 41642: The directions for the problem is "Solve each equation for x to three significant digits” the problem is . I tried changing it to but I couldn’t find anywhere to go after that. I would appreciate if you could help me figure this one out. Please and thanks!
Click here to see answer by fractalier(2101)

Question 42238: Find the domain and range of the function: y=1/2(2)^x.
Click here to see answer by fractalier(2101)

Question 42247: Solve (1/81)^t = 243^t-2.
Thanks
Click here to see answer by fractalier(2101)

Question 42251: Write the equation log(243) 81=4/5 in exponential form.
Click here to see answer by fractalier(2101)

Question 42263: Solve: 4+3e^(5x)= 27.
Tjank you
Click here to see answer by fractalier(2101)

Question 42266: At a town with a large convention center, the cost of a hotel room has increased 5.1% annually. If the average hotel room cost $48.00 in 1980 and this growth continues, what will an average hotel room cost in 2012?
Use y=a(1+r)^t and round to the nearest cent.
Click here to see answer by fractalier(2101)

Question 42265: A particular compound decays according to the equation y=ae^(-0.974t), where t is in days. Find the half-life of this compound.
Click here to see answer by fractalier(2101)

Question 42264: Solve 1n (x+5) >or= 2.
Thank you
Click here to see answer by fractalier(2101)

Question 42262: Evaluate: 1n e^(-9x).
thank you
Click here to see answer by fractalier(2101)

Question 42260: Solve 5^(2x+1) >or= 50.
Click here to see answer by fractalier(2101)

Question 42261: Use common logarithms to approximate log(9) 207 to four decimal places.
Click here to see answer by fractalier(2101)

Question 42258: Solve log(4) (m-3) + log(4) (m+3)=2.
thanks
Click here to see answer by fractalier(2101)

Question 42257: Use log(5) 2≈0.4307 and log(5) 3≈0.6826 to approximate the value of log(5)=54.
thanks
Click here to see answer by fractalier(2101)

Question 42255: Solve log(2) (7x-3)>or=log(2) (x+12).
Thank you
Click here to see answer by fractalier(2101)

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