Questions on Algebra: Exponent and logarithm as functions of power answered by real tutors!

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Algebra: Exponent and logarithm as functions of power

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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(958)

Question 39577: Multiply.
4xy^3*2x^2*5xy^2
Click here to see answer by AnlytcPhil(958)

Question 39615: Write the answer without negative or zero exponents: a-3
Click here to see answer by AnlytcPhil(958)

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(8405)

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(4898)

Question 39671: The volume of a spehere can be given by the formula V=4.18879rcubed
Click here to see answer by fractalier(1804)

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(26259)

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(3495)

Question 40006: log(5)625+log(9)(x-3)=6 need help please
Click here to see answer by fractalier(1804)

Question 39984: log4(2x+3)-logx=3
Click here to see answer by fractalier(1804)

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(1804)

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(1804)

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(26259)

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(26259)

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(26259)

Question 40817: 3(1.3^x)=X^2-2
Click here to see answer by stanbon(26259)

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(1804)

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(456)

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(4898)

Question 41300: I am getting stuck on this one:
1/8=4^5x-2
Please Help
Click here to see answer by psbhowmick(456)

Question 41370This question is from textbook

: 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?This question is from textbook

Click here to see answer by venugopalramana(3286)

Question 41642This question is from textbook Algebra with trigonometry
: 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! This question is from textbook Algebra with trigonometry

Click here to see answer by fractalier(1804)

Question 42238: Find the domain and range of the function: y=1/2(2)^x.
Click here to see answer by fractalier(1804)

Question 42247: Solve (1/81)^t = 243^t-2.
Thanks
Click here to see answer by fractalier(1804)

Question 42251: Write the equation log(243) 81=4/5 in exponential form.
Click here to see answer by fractalier(1804)

Question 42263: Solve: 4+3e^(5x)= 27.
Tjank you
Click here to see answer by fractalier(1804)

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(1804)

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(1804)

Question 42264: Solve 1n (x+5) >or= 2.
Thank you
Click here to see answer by fractalier(1804)

Question 42262: Evaluate: 1n e^(-9x).
thank you
Click here to see answer by fractalier(1804)

Question 42260: Solve 5^(2x+1) >or= 50.
Click here to see answer by fractalier(1804)

Question 42261: Use common logarithms to approximate log(9) 207 to four decimal places.
Click here to see answer by fractalier(1804)

Question 42258: Solve log(4) (m-3) + log(4) (m+3)=2.
thanks
Click here to see answer by fractalier(1804)

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(1804)

Question 42255: Solve log(2) (7x-3)>or=log(2) (x+12).
Thank you
Click here to see answer by fractalier(1804)

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