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 60566: whats the square root of 18m to the 5th n to th 6th?????
Click here to see answer by tutorcecilia(2152)

Question 60825: Please help me with the following problem:
2log(y+2)=log(y+2)-log12
What I tried -
log(y+2)-log12-log(y+2)^2
y+2/12(y+2)^2=1
y+2/12y^2+48y+48=1
y+2=12y^+48y+48
12y^2+47y+46=0
That's where I got! - please help!
Click here to see answer by Nate(3500)

Question 60830: how do i solve this please explaon!!!!!!! i have a test on tuesday and its already saturday and i dont know how to do it
Click here to see answer by checkley71(8403)

Question 61141: my question is
y varies jointly as m and the square of n and inversely as p. y =15 when m=2, n=1, and p=6. Find y when m=3, n=4 and p=10
Click here to see answer by stanbon(57246)

Question 61302: Solve, ln(lnx)=2
Click here to see answer by funmath(2925)

Question 61305: Solve, ln x^1/4 = (ln x)^1/2
Click here to see answer by venugopalramana(3286)

Question 61304: Solve, ln x^1/4 = (ln x)^1/2
Click here to see answer by venugopalramana(3286)

Question 61669: The half- life of a radioactive substance is one hundred ninety-four days. How many days will it take for eighty percent of the substance to decay?
I used the half life decay formula.
my formula for the problem read...
0.8Nsubscript0=Nsubscript0*(1/2)superscript(t/194)
the result was about 62.5,
is this correct.
=]
Click here to see answer by Edwin McCravy(8882)

Question 61670: The half- life of a radioactive substance is one hundred ninety-four days. How many days will it take for eighty percent of the substance to decay?
I used the half life decay formula.
my formula for the problem read...
0.8Nsubscript0=Nsubscript0*(1/2)superscript(t/194)
the result was about 62.5,
is this correct.
=]
Click here to see answer by ankor@dixie-net.com(15638)

Question 61664: I need help on this homeowrk question. Thank you!
FOr each of the following relations, sketch the graph of the relation and its inverse and write an eqation for the inverse.
y=x squared -2x-3
I can graph it using my calculator but i cant seem to figure out the inverse equation
Click here to see answer by stanbon(57246)

Question 61856: Please find dy/dx using implicit differentiation:
y^2+e^y=ln x^2+4
Thanks!
Click here to see answer by funmath(2925)

Question 61855: Could someone please help me solve:
4^(2-6x)=812
Click here to see answer by prmarella(3)

Question 61855: Could someone please help me solve:
4^(2-6x)=812
Click here to see answer by funmath(2925)

Question 61872: Solve the equation 2^3x=4^x-1 by getting a common base.
Click here to see answer by funmath(2925)

Question 61854: I am having trouble solving these problems could someone help me?
7^2x+3=49^8-x
Click here to see answer by funmath(2925)

Question 61949: Can you help me with this question?
Rewrite this equation ---> 2logt+1.4=3logd <--- without logarithms and with t as the subject.
Thanks a lot!
Click here to see answer by stanbon(57246)

Question 61916: 2
X + 7X+9=0
Click here to see answer by chitra(359)

Question 61869: 1)y=-2/3x
2)y=-2x+5
3)log34/h
4)log3c5d
Click here to see answer by funmath(2925)

Question 61834: Exponential and Logarithmic Functions
(1)Let f(x) = 2^x , g(x) = (1/8)^x, and h(x) = log sub 2(x). Find each of the following:
f(3)
f(-2)
f(1/2)
g(2)
g(-1)
g(1/3)
h(2)
h(1/2)

(2) Solve each of the following equations for the given variable
(a) 2^a = 16
(b) 3^z = 1/9
(c) 9^n = 3
(d) (1/5)^x = 25

Click here to see answer by funmath(2925)

Question 61836: Exponential and Logarithmic Functions
(1) Let f(z) = 3^z
(a) Find what value of z does f(z) = 81?
(b) For what value of z does f(z) = 1?
(2) Graph each of the following. Give coordinates of at least 3 points on each graph.
(a) y = 3^x
(b) y = logsub 3 x
(3) The population of a large U.S. city is growing according to the function P = 1,400,000(1.023)^t, where t is the number of years since 1990.
(a) What was the population in 1990?
(b) What will the population be in 2007 according to this formula?
(c) What does the value of 1.023 mean in the context of the problem?
Click here to see answer by funmath(2925)

Question 62034: PLEASE SOLVE THIS. IT SEEMS LONG BUT I SOLVED HALF OF IT ALREADY. I JUST NEED HELP ON THE LAST HALF. PLEASE. I WOULD REALLY APREACIATE IT.
Exponential-and-logarithmic-functions/62014 (2006-11-18 15:20:14): Rabbit Problem: When rabbits were first brought to Australia last century, they had no natural enemies so their numbers increased rapidly. Assume that there were 60,000 rabbits in 1865, and that by 1867 the number had increased to 2,400,000. Assume that the number had increase exponentially with the number of years that elapsed since 1865.
a) Write the particular equation for this function.
b) How many rabbits would you predict in 1870?
c) According to your model, when was the first pair of rabbits introduced into Australia?
d) Based on the properties of exponential functions, why is it appropriate to say that the rabits "multiplied?"
What I had done so far:
a) I had pluged the information into my graphing calculater in the STAT section. My x variable was the number of years after 1865 (because if I did plug in the whole years then it would overflow, so the year 1865 was 0 and 1867 was 2). The y variable was the number of rabbits. After I plugged it in, i got an equation: y=60,000*6.32455532^x
b) I plugged 5 for x and I got about 607,157,310 for my answer.
c) This is when I got into trouble.
I replaced y with 2 and then I changed the equation to log form: x=60,000*log of base 6.32455532 of 2 (because c=a^b also means b=log of base a of c). Then I got 22548.21897 but that doesn't fit so I don't know what to do.
PLEASE HELP
Click here to see answer by stanbon(57246)

Question 61674: Please help !!!
a sum of 100,000 is invested in a bank at a rate of 6 % p.a .
a)assume the amount of money invested for 5 years .
b)detemine the amountthat will be withdrawn if the compunding will be done
i) once a year ii) monthly iii) continously
formula ;
A = p ( 1+r) ^ n
Click here to see answer by stanbon(57246)

Question 62091: solve the equation 4^2x+1=2^3x+6
this is what I did.

(2^2)^2x+1=2^3x+6
2^4x+1=2^3x+6
4x+1=3x+6
x=5
IS this correct?
Click here to see answer by joyofmath(189)

Question 62091: solve the equation 4^2x+1=2^3x+6
this is what I did.

(2^2)^2x+1=2^3x+6
2^4x+1=2^3x+6
4x+1=3x+6
x=5
IS this correct?
Click here to see answer by Earlsdon(6287)

Question 62199: I tried solving this problem, but I don't know where to start.
6 ln e^-3
Click here to see answer by josmiceli(9661)

Question 62377: I have tried to set this one up but have been unsuccessful. Can anyone help me out?
Find each value of x.
log4 x = 1/2
the 4 next to the log in like an exponent but shows below it. Thanks!
Click here to see answer by Earlsdon(6287)

Question 62378: This says to use a calculator to find the value to four decimal places.
1n 0.005.
and then separately find y to four decimal places if possible.
log y = 0.926
I am absolutely clueless on these although I have reviewed it in the book. Can anyone help me out?
Click here to see answer by Earlsdon(6287)

Question 62376: I have tried to set this one up but have been unsuccessful in getting the solution. Can anyone help me out?
Find each value of x.
log1/2 16 =x
the 1/2 next to the log in like an exponent but below it. I hope it is clear enough. Thanks in advance!
Click here to see answer by stanbon(57246)

Question 62313: I need to find the closed form of this recursive function: a(n)= 5*a(n-1) where a(0) is the initial value?
Click here to see answer by joyofmath(189)

Question 62418: find the constant rate of increase k, when the expotential function consist of x values of 0,1,2,3,4,5. and y values 2,4,8,16,32,64
Click here to see answer by uma(370)

Question 62416: A population is increasing at a rate of 0.6% each year. The population is currently 3000. Find a function p(t)that gives the size of the population t years from now.

Click here to see answer by jai_kos(139)

Question 62314: A population is increasing at a rate of 0.6% each year. The population is currently 3000. find the function p(t)that gives the size of the population t years from now.

Click here to see answer by jai_kos(139)

Question 62315: A model for the number of people N in a college community who have heard a rumor is: N= P*(1-e^-0.15d)
where P is the total population of the community and d is the number of days that have elasped since the rumor began. In a community of 10,000 students, how many students will have heard the rumor after 3 days?
Click here to see answer by ankor@dixie-net.com(15638)

Question 62458: (((log10X=1000))) new to logarithms
Click here to see answer by stanbon(57246)

Question 62493: Can anyone give me a hand with this one? Thanks
Solve the equation. If answer is not exact,givethe answer to four decimal places.
27^x+1 = 3^2x+1
Thanks for your assistance.
Click here to see answer by josmiceli(9661)

Question 62499: Did I complete this correctly? Thanks for checking.
PH of sour pickles question:
The hydrogen ion concentration of sour pickles is 6.31 x 10^-4. Find the PH.
pH= -log [H^+]
pH= -log 10^-4
= -(-4)log10
= -(-4)multiplied by 1
using property 2 of logarithms: logb b=1
= 4
Click here to see answer by stanbon(57246)

Question 62498: I am lost on this one. Is there anyone that help me out? Thanks
Assume that x, y, z and b are positive numbers. Use the properties of logarithms to write each expression in terms of logarithms of x, y and z.
log b x^1/2y^3
The b is right next to the log but slightly below. Hope you understand. Thanks again!
Click here to see answer by stanbon(57246)

Question 62631: A population is increasing at a rate of 2% each year. The population is currently 5000. Find a function p(t) that gives the size of the population t years from now.
Click here to see answer by stanbon(57246)

Question 62614: the amount of radioactive tracer remaining after t days is given by A=A0e^-0.18t, where A0 is the starting amount at the beginning of the time period. How much could be acquired now to have 40 grams remaining after 3 days?

Click here to see answer by ankor@dixie-net.com(15638)

Question 62632: A culture of bacteria obeys the law f(t)= f(0)*e^0.47*t. If 500 bacteria are present initially , and there are 800 after 1 hour, how many will be present in the culture after 5 hours?
Click here to see answer by ankor@dixie-net.com(15638)

Question 62635: Find the closed form of the following recursive function: a(n)=5*a(n-1) where a(0) is the initial value.
Click here to see answer by joyofmath(189)

Question 62612: find an exponential function of the form f(x)=ba^x+c with y- intercept 2, horizontal asymptote y=-2, that passes through the point P(1,4)
Click here to see answer by venugopalramana(3286)

Question 62464: Given that a set of data has a constant ratio of 8 and an initial value of 6, what is the rate of increase k?
Click here to see answer by dolly(163)

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