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 562787: Please help me solve this:
2^-x=1.5
I tried this:
ln2^-x=ln1.5
-xln2=ln1.5
-x=ln1.5/ln2
x=-0.585
Thanks
Click here to see answer by issacodegard(60)

Question 563321: Find the value of the expression. Do not use decimals.
(1/3)log54+2log15+(1/3)log32-3log3
All the bases are 10
Click here to see answer by stanbon(75887)

Question 563670: Please help with this. I can't understand the way my teacher is trying to explain.
Let "b" be a number such that log(b)3 = 1.5 and log(b)5=2.2
evaluate the following:
1. log (b)5/3
2. log (b)3b^2
3. log (b)45
4. log (b)(b/15)
Thank you so much for your help
Click here to see answer by josmiceli(19441)

Question 563705: Please help with this. I can't understand the way my teacher is trying to explain.
Let "b" be a number such that log(b)3 = 1.5 and log(b)5=2.2
evaluate the following:
1. log (b)15
2. log (b).6
3. log (b)125
4. log (b)(^3sqrt(3))^7
Thank you so much for your help
Click here to see answer by Alan3354(69443)

Question 563869: Help! Graph y=3e^x
Click here to see answer by Theo(13342)

Question 563928: Please help me solve this: Suppose that ln 2=a and ln 3=b use the properties of logarithms tro write each logarithm in terms of a and b.
ln27
Thanks
Click here to see answer by josmiceli(19441)

Question 564990: Someone bought a CD player for $250 and finds 2 years later when he wants to sell it that it's worth $100. Find a formula for the value of the CD player if the value decreases.
Click here to see answer by stanbon(75887)

Question 565053: how do i solve and check
4^2x=32^1/2
Click here to see answer by ad_alta(240)

Question 565426: how do i solve rational exponents and evaluate like 16 -3/2
Click here to see answer by Alan3354(69443)

Question 565529: Please Help with this. My teacher did not explain how to do these problems.
Use the formula D^3 = 216T^2
1. Find what happens to the duration of a storm if its diameter is doubled.
2. determine how long a storm will last if it has a diameter of 10 mi.
Thank you so much.
Click here to see answer by stanbon(75887)

Question 565892: if log(x+1) + log(x-1) = 5, then what expression is equal to 10^5
Click here to see answer by stanbon(75887)

Question 467405: A grandmother is looking for a plan to finance her new grandchild�s college education. She has $25,000 to invest. Search the internet and locate a long-range investment plan, CD, Savings Bond, etc, for the grandmother. The plan is to earn compound interest.
Calculate the future value of the investment. You must use the advertised interest rate,which is 3.40% the number of compounding periods per year,which and the time the funds will be invested. If you are not given the number of compounding periods a year, make it up.
The principal is $25,000. This is P.
Research the annual interest rate for your investment. This is r.
State the time in years for the investment (as in when the new grandchild will be attending college) which is 18. This is t.
State the number of compounding periods per year.2, This is n.
Model the future value of Grandma�s investment as an exponential function, with time as the independent variable: F(t) = P(1 + r/n) nt
State the future value of Grandma�s investment.
Use the internet or library resources to find the average cost of a college education today; will grandma�s investment be able to cover the cost in today�s dollars; what about in the future?
Summarize your findings in writing using proper style and grammar.

Click here to see answer by deeakram(1)

Question 566011: Potassium 42 has a decay rate of approximately 5.5% per hour, assuming an exponential decay model, fine the number of hours it will take for the original quantity of potassium 42 to b halved?
Click here to see answer by stanbon(75887)

Question 566009: potassium 42 has a decay rate of approxmiately 5.5% per hour, assuming an exponential decay model, find the number of hours it will take for the original quantity of potassium 42 to be halved?
Click here to see answer by stanbon(75887)

Question 566148: I am having difficulty comprehending how this is done. Please Help!
Use the formula v= 4/3 pi r^3
1. If the radius of a ball is twice that of another, how many times as big is its volume?
2. If the volume is twice that if a blue ball, how many times as big is its radius?

Thank you
Is
Click here to see answer by Alan3354(69443)

Question 566524: find r if 0.1145=r cubed

Click here to see answer by rfer(16322)

Question 566764: Natural log base of e to the -4
Click here to see answer by solver91311(24713)

Question 567762: solve for x: log2(x+2) + log2(x+6)=5
Click here to see answer by lwsshak3(11628)

Question 567785: Given logk 3=7, logk 4=13, and logk 5=22, find logk (12/5k^3)^2
Click here to see answer by solver91311(24713)

Question 567783: solve for x: 8ln(1/2x)=72
Click here to see answer by rapaljer(4671)

Question 568663: I'm not entirely sure this is the right subject, sorry if it's not...
A substance decomposes radioactively. Its half-life is 32 years. Find the constant "k" in the decay formula.
Use this formula instead:
y= final value
n= initial value
k= constant
t= time
e= antilogarithm
Click here to see answer by solver91311(24713)

Question 569183: Please help!!I have been working on these for hours.
Solve each equation:
a. ln(2x-1)=3
b. log x = 1/10,000
c. ln(2x-1) = 3
d. ln(x+3) = 1
Thank you so much!!
Click here to see answer by Tatiana_Stebko(1539)

Question 570869: solve each equation. Round to four decimal places.
2^n=sqrt(3^n-2)
Click here to see answer by Alan3354(69443)

Question 571056: rewrite equation in exponential form log u 15/16 = v
Click here to see answer by nyc_function(2741)

Question 571057: rewrite equation in logarithmic form
64 1/2 = 8
Click here to see answer by stanbon(75887)

Question 571058: show that log8 1000=log2 10 algebraically
Click here to see answer by stanbon(75887)

Question 571114: Write an exponential function for a graph that includes point (1, 0.84) and (2,1.008). I've gotten as far as 0.84/b=a , and 1.008=(.84/b)*b^2, but I'm stuck there.
Click here to see answer by KMST(5328)

Question 571504: how to solve
299^99
Click here to see answer by Alan3354(69443)

Question 571605: A substance has a life of 1,523 years .What is fraction of the substance would be left after 10,000 years ?
Click here to see answer by KMST(5328)

Question 571607: A substance has a half life of 23 hours .How old is the object that has 5% of the substance left?

Click here to see answer by ankor@dixie-net.com(22740)

Question 572190: If log9/logx=1/2 what is the value of x?
Click here to see answer by Alan3354(69443)

Question 572625: how do i find the rational zeros of P(x) = x3 − 8x2 + 17x − 10
Click here to see answer by lwsshak3(11628)

Question 571838: For the given functions f, g , and h , find f o g and state the exact domain of f o g o h .
f(x) = e^x
g(x) = logx
h(x) = x/x + 8

Click here to see answer by lwsshak3(11628)

Question 572538: Carbon-14 has a half life of 5760 years. How old is a fossil that has 1/8 of the substance left?

Click here to see answer by KMST(5328)

Question 574029: 8 with an exponent of 4/3
Cubed sq root of 5 over cubed sq. root over 5
Click here to see answer by stanbon(75887)

Question 574650: Ok, so I just want to know the method of finding the base of a logarithm. I am given a picture of a graph; two points of a function, (3,5) and (5,9); and the asymptote: x=2 . I see that there are 6 variables for me to find, and that I am given 5 numbers to "plug" in. I see how the graph points (3,5) and (5,9) fit into the equation y=alog↓b(x-h)+k, but I don't understand how to put the asymptote into the equation or how to find base b. Is there a specific way to find base b of a graph using these?
Click here to see answer by KMST(5328)

Question 575203: How do you solve for E in the following equation?
9=0.67log(0.37E)+1.46
Click here to see answer by josmiceli(19441)

Question 575448: what is the value of x? please explain by showing work
2 - Log 3x = Log (x/12) + 2
Click here to see answer by solver91311(24713)

Question 576749: The half-life of a radioactive substance is the time it takes for half of the substance to decay. The half-life if carbon-14 is 5700 years.
A.) write a exponential function to model the decay of a 240-my sample.
B.) explain what each value in the function model represents.
C.) to the nearest hundredth, find the amount of carbon-14 remaining after 2353 years. Explain how you found this amount.
Click here to see answer by ankor@dixie-net.com(22740)

Question 577014: what is pi
Click here to see answer by Alan3354(69443)

Question 577594: What is n^x =x ?
Click here to see answer by Alan3354(69443)

Question 577833: (x+7)^(2/3)=9
I got 20 as one solution for x and I know it's correct, but I'm supposed to find a second one as well. please help
^(2/3) means *to the power of 2/3* in case that was confusing
Click here to see answer by Alan3354(69443)

Question 578260: A business has a $20,000 profit in 1990. The profit increased by 20% per year for the next 10 years. Write an exponential growth model.
Click here to see answer by dfrazzetto(283)

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