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 617629: Please help Find the domain of the function.
f(x) = log4(x - 4)^2
Click here to see answer by lwsshak3(6764)

Question 617944: Please help solve the problem.
The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential growth model A = 4800e0.055t. How much did you initially invest in the account?
Click here to see answer by Theo(3504)

Question 617942: Please help express as a single logarithm.
(loga q - loga r) + 4loga p
Click here to see answer by Theo(3504)

Question 617969: Please help solve the problem.
The logistic growth function f(t) = 440/1=6.3e-0.28t describes the population of a species of butterflies after they are introduced to a non-threatening habitat. What is the limiting size of the butterfly population that the habitat will sustain?
Click here to see answer by Theo(3504)

Question 617971: Solve the problem.
The logistic growth function f(t) = 400/1+9.0e-0.22t describes the population of a species of butterflies after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 12 months?
Click here to see answer by Theo(3504)

Question 617974: Please help solve the problem.
Which of the two rates would yield the larger amount in 1 year: 9 1/4% compounded monthly or 9% compounded annually?
Click here to see answer by Theo(3504)

Question 617982: Find the amount that results from the investment.
$12,000 invested at 11% compounded quarterly after a period of 4 years
Click here to see answer by mananth(12270)

Question 617940: 2x+y=4
Click here to see answer by lynnlo(4169)

Question 617985: Solve the problem.
The half-life of silicon-32 is 710 years. If 100 grams is present now, how much will be present in 600 years? (Round your answer to three decimal places.)
Click here to see answer by nerdybill(7011)

Question 618084: Identify the important characteristics of an exponential function. Explain the difference between the graph of an exponential growth function and an exponential decay function and give an example of each type of function.
Click here to see answer by solver91311(17077)

Question 618186: Hello, can someone please help me..I cannot wrap my head around this problem.
if f(x)=ln x, g(x)=e^(7x), and h(x)=x^6 find the following
1. (fog)(x) and domain of (fog)(x)
2. (gof)(x) and domain of (gof)(x)
3. (fog)(x) and domain of (foh)(x)
I tried to start them out but I am completely stumped!
1). (fog)(x)=f(g)x))= lnx(e^(7x))
2). (gof)(x)=g(f(x))=e^(7x)lnx))
3.) (foh)(x)=f(h)x))=lnx(x^6)

I can usually figure out the composite functions but the exponential and logarithm has me really confused.
Thanks a ton!
Click here to see answer by stanbon(57984)

Question 618258: 2log[4](3x)+log[4](11)=14
Solve. I don't know how to. The answer I could come up with is
2log[4](3)+2log[4](x)+log[4](11)=14
But I don't think that's right. Is it?
Click here to see answer by lwsshak3(6764)

Question 618402: Pleas help solve the equation.
8 + 4 ln x = 5
Click here to see answer by ewatrrr(10682)

Question 618401: ``Please help solve the problem.
The logistic growth function f(t) = 440/1+6.3e-0.28t describes the population of a species of butterflies after they are introduced to a non-threatening habitat. What is the limiting size of the butterfly population that the habitat will sustain? ''.
Click here to see answer by josmiceli(9817)

Question 618721: log3243
Click here to see answer by josmiceli(9817)

Question 619232: what is the solution to log (6x-2)-log (x-3)=1
Click here to see answer by Theo(3504)

Question 619389: sketch y= -log5(-x) by first describing the transformation performed on the equation y=log5(x)
find the eqution of the inverse function
sketch theinverse fuction on the same axes
Click here to see answer by Theo(3504)

Question 619865: how would you solve this equation?
2√5+1 -9=3
Click here to see answer by jim_thompson5910(28717)

Question 619836: Solve 3x = 69. Round your answer to the nearest hundredth.
Click here to see answer by Alan3354(31538)

Question 620588: Solve the exponential equation.
2x = 1/2
3x = 1/27
2-x = 16
4x = 0.5
8x = 1/4
Click here to see answer by Alan3354(31538)

Question 620588: Solve the exponential equation.
2x = 1/2
3x = 1/27
2-x = 16
4x = 0.5
8x = 1/4
Click here to see answer by lynnlo(4169)

Question 621223: 22. Which are upper and lower bounds for the real roots of 3x4 − 2x3 + x − 9 = 0?
A. 0 and 3

B. –2 and 2

D. –3 and –1, 1, and 3

Click here to see answer by lwsshak3(6764)

Question 621220: 13. Solve 2x = 5x2 for x.
A. 0 and 0.431

B. 0 and 2.322 (this answer is wrong)

C. 2.322

D. 0.431

Click here to see answer by unlockmath(1614)

Question 621333: i do not know how to express as a single logarithm
heres the problem:
6 log[m](p) - 5 log[m](q)2

Click here to see answer by lwsshak3(6764)

Question 621718: what is the base of log(6)
Click here to see answer by lynnlo(4169)

Question 622093: 22e^2x=192.5
Click here to see answer by jim_thompson5910(28717)

Question 622525: solve the equation and round your answer(s) to the nearest hundredth.
e^x-1 = 2x+1
Click here to see answer by solver91311(17077)

Question 622548: The question asks to "tell whether the x-value is a solution of the equation" answer yes or no. I have no idea how to go about these. Thanks in advance!
lnx=3,x=e^3
lnx=4,x=4^e
lnx=5,x=5^e
log5x=2,x=20
Click here to see answer by solver91311(17077)

Question 622867: Hello ,
solve this equation please:
log(x+7) = 1
Click here to see answer by Alan3354(31538)

Question 622878: Please solve:
8^(x+1) = 3^2x
note that (x+1) and 2x are exponents
Thank you
Click here to see answer by josmiceli(9817)

Question 622906: Write in exponential form.
ln1= 0
Click here to see answer by Alan3354(31538)

Question 622911: solve:
logx + log(x+3)= 1
Click here to see answer by nerdybill(7011)

Question 622913: write in exponential form:
lnx= 4
log3 1/81 =4
note- 3 is an exponent down
Click here to see answer by nerdybill(7011)

Question 622918: solve:
e^(x+1) = 20
log(x^2 + 19) = 2
logx + log(x+3) = 1
Click here to see answer by lwsshak3(6764)

Question 622917: write as a single logarithm:
3logX + 1/2logY
2(logX- logY)
log(X+4) + log(X-3)
ln(2X-1) - ln(X+3)
Click here to see answer by lwsshak3(6764)

Question 622914: writein logarithmic form:
10^0 =1
y=e^x
Click here to see answer by lwsshak3(6764)

Question 622916: use the properties of logarithms to expand:
ln square root of X over Y to the fourth power
Click here to see answer by lwsshak3(6764)

Question 622915: Use the properties of logarithms to expand:
log x^2y^3/z
ln (x^1/2 y^1/4)
Click here to see answer by lwsshak3(6764)

Question 622908: use the properties of logarithms to expand:
log(mn)squared
Click here to see answer by lwsshak3(6764)

Question 622907: Write in logarithmic form:
e to the first power = 2.718
Click here to see answer by lwsshak3(6764)

Question 622910: write as a single logarithm:
3logx + 1/2logy
Click here to see answer by nerdybill(7011)

Question 622964: In the expression log3_x=2, identify the base of the log, the argument, and the exponent. Rewrite this expression into exponential notation.
Click here to see answer by Alan3354(31538)

Question 623003: Solve the equation 7^(x – 2) = 5^x. Round the answer to four decimal places.
Click here to see answer by MathTherapy(1484)

Question 623003: Solve the equation 7^(x – 2) = 5^x. Round the answer to four decimal places.
Click here to see answer by lwsshak3(6764)

Question 623001: Solve the equation 7^(x – 2) = 5x. Round the answer to four decimal places.
Click here to see answer by Alan3354(31538)

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