Questions on Algebra: Logarithm answered by real tutors!

Tutors Answer Your Questions about logarithm (FREE)

Question 4865: Change log10 into logarithm in base 2
Click here to see answer by longjonsilver(2297)

Question 4867: To expand the logarithmic expression as much as possible:
In x^3/(x-3)^2
Solve:
log10 (x-30)= 3- log10 x

Click here to see answer by longjonsilver(2297)

Question 4895: log (6x + 5) - log 3 = log 2 - log x

Click here to see answer by rapaljer(4667)

Question 4895: log (6x + 5) - log 3 = log 2 - log x

Click here to see answer by arunpaul(104)

Question 4561: Please help! I can not figure out two problems. I am to determine whether the following system is consistent, inconsistent, or dependent. If the system is consistent, find the solution of the system.
The first problem is :
6x + 4y =8
9x + 6y =12

and the second problem is:
2/3x + 3/4y =4
5/6x - 3/8y = -11/2

Click here to see answer by Abbey(339)

Question 4988: Can you please explain how to this works out: ,
Click here to see answer by ichudov(499)

Question 5114: Hi, I need help with this: Use the properties of logarithms to expand the expression as much as possible without using a calculator. log x^-4a
Click here to see answer by rapaljer(4667)

Question 5113: y=e^10^2x
x=?
Click here to see answer by rapaljer(4667)

Question 5155: I need help solving the following...
ln(x)^(ln(x))=4
so far I took both sides times "e" to get...
e^ln(x)^(ln(x))=e^4
x^(ln(x))=e^4
but I don not know what to do next!!
Thanks for the help
Click here to see answer by khwang(438)

Question 5276: 2
: Please help me with this problem.
Click here to see answer by Earlsdon(6287)

Question 5299: How do I approach, and solve, this problem?:
2^logX + 3^logY = 2^log(X+1) + 3^log(Y+1)
Solve for X
Click here to see answer by arunpaul(104)

Question 5387: I am sending two questions, because I think they are very similar, although I was able to solve only the first one, but in a somewhat unsatisfactory way:
1)
2)
My goal would be to solve these inequalities purely by algebraic manipulation.
I examined both questions with Mathematica 4 and graphed them with Winplot (Peanut)and both confirm the answers, that by coincidence are the same for the two questions.
I would very much appreciate some help here.
Thanks
Andreas

Click here to see answer by longjonsilver(2297)

Question 5515: Jon
Thanks for the quick reply on my question (# 5387)
Unfortunately, because this text screen "went berserk" when I posed my question I was unable to relate all what I had done and had to erase my explanations and simplify my question
The answer to both problems is: true for x between zero and one and x greater/equal to two
The algebra manipulation you made is all right but, as you can see from the answer(s), only part of the solution
I was looking for the sistematics to find the above answer by purely manipulating algebra and had no success, why I asked you
Both questions have the same answer and in both cases I verified them by other means, like graphing and mathematica 4
Look forward to be hearing from you again
Thanks
Andreas
Click here to see answer by longjonsilver(2297)

Question 5880: How do I find the X coordinate of the equation e^x+2 -4
Click here to see answer by longjonsilver(2297)

Question 5894: I'm trying to figure out how to plot the graph y=ln(1-x) by shifting the basic graph for y=ln(x). including the equation of the asymptote, and the coordinates of the y-intercept. Can I think of it as y=ln(-x+1)? Then I could reflect the graph across the y axis and shift it up 1? Would that work?
Click here to see answer by longjonsilver(2297)

Question 5851: I am unable to solve this problem. Kindly help.
Log10(x+y)/3 = 1/2(log10x + log10y) Now, prove that x/y + y/x = 7
Click here to see answer by longjonsilver(2297)

Question 5994: This equation is giving me issues.
log(base2)(x-6)+log(base2)(x-4)-log(base2)x = 2
Solve for x. Reject any value of x that produces the logarithm of a negative number or 0.
What I've done:
log(base2)(x-6)(x-4)-log(base2)x = 2
log(base2)(x-6)(x-4)/x = 2
(x-6)(x-4)/x = 2^2 = 4
4 = (x-6)(x-4)/x
There is where I am stuck.
Some help on this would be great. Thanks.
Click here to see answer by prince_abubu(198)

Question 6108: write each expression as the sum or difference of logarithms. express powers as factors
ln(x^4sqrtx^2+1) Thank you!!
Click here to see answer by Abbey(339)

Question 6114: use change of base formula and calculator to evaluate. round to 3 decimal places

log(base5)18
Click here to see answer by Abbey(339)

Question 6115: use change of base formula and calculator to evaluate. round to 3 decimal places
log(base1/2)15
Click here to see answer by Abbey(339)

Question 6116: use change of base formula and calculator to evaluate. round to 3 decimal places
log(basesqrt5)8

Click here to see answer by Abbey(339)

Question 6276: what is scientific notation?
Click here to see answer by xcentaur(357)

Question 6315: This word problem has me stomped.
When a 26 foot ladder is leaned on a house, the distance from the base of the ladder to the house is 14 ft less than the distance from the top of the ladder to the ground. How far up the side of the house is the ladder?
Click here to see answer by Earlsdon(6287)

Question 6392: I am having a problem with radicals and not really sure how to solve this problem since the square root of 20 doesn't come out to be a whole number. Heres the problem...
what is the square root of 20x^5
Thank You for any help.
Joe
Click here to see answer by rapaljer(4667)

Question 6480: This question has three parts (a,b,c)
a) Find the inverse of the function.
b) State the domain of the function and the domain of its inverse.
c) Use property of inverse functions to show your inverse is, in fact the inverse of the function.
f(x)=log(4x)+log((3+x)/x^2)

Click here to see answer by khwang(438)

Question 6432: Can someone just tell me if I am right? If 30 cents out of every 1 dollar goes to taxes, and the rest is net income, what is the ratio of taxes to net income?
I think the answer 3:7. Is that right?
Click here to see answer by minerva(22)

Question 6427: I am having trouble with this question. I think I know the answer but I am not sure. My question is Fifty people own 4,000 books. What is the ratio of people to books. I think the answer is 1:80, Is that right?
Click here to see answer by minerva(22)

Question 6549: I having a problem working this problem out, I am trying to FOIL it, but not sure I am coming up with the right answer or if I am missing something.
Heres the problem...
square root of 5 ( square root of 3 + square root of 2 )
Thank you for any help you may provide.
Click here to see answer by longjonsilver(2297)

Question 6575: I am looking for the inverse of the function y= 3x -1, where x is the power. So it is read, y equal to 3 to the power of x -1. I know the inverse should be in logarithmic form, but I'm not sure whether I log an entire side or not. Then I am suppose to graph the inverse, stating domain and range.
Can you help me?
Thanks.
Click here to see answer by ichudov(499)

Question 6587: I can't figure out the solution to this equation, or if a real solution really exists.
Click here to see answer by Mike(39)

Question 6587: I can't figure out the solution to this equation, or if a real solution really exists.
Click here to see answer by ichudov(499)

Question 6629: How do I solve the equation,
Click here to see answer by prince_abubu(198)

Question 6634: Hi,I really appreciate you trying to help me!! I have this question that I do not really know how to answer, so I hope you can help me, please!!

where 1 is less than x and less than y, is the answer positive or negative???
I think that I am supposed to sub in a number less than 1 in both x and y and see what the sign of the final answer is????? I hope you can help me and thank you!!!!
Click here to see answer by khwang(438)

Question 6596: I am having dificulty solving logirithms once I put them in exponential form and vice versa. Here is the question I am confused on LOGx 16=4/3

Click here to see answer by rapaljer(4667)

Question 6426: I am having trouble with this question. Suppose a family starts out 50 miles from home at time t=0. They travel away from home at a constant speed of 45 miles an hour. What's the equation that tells you how far they'll be from home t hours later? ( Assume d is distance in miles.)
Click here to see answer by xcentaur(357)

Question 6701: I tried this natural log problem and keep comming up with the wrong awnser of .25 HELP! (please)
Am i just bad at algebra or is this somewhat complicated
Click here to see answer by ichudov(499)

Question 6717: I am horrible when it comes to word problems. I have been at this for two hours now and cannot come up with a solution. Can anyone help? It is as follows:
Using the formula of R=log(I/Io) for Richter scale:
The strongest earthquake ever to strike Japan occurred in 1933 and measure 8.9 on the Richter scale. How many times more severe was this 1933 quake than the one in May 1983 which measured 7.7 on the Richter scale?
Click here to see answer by prince_abubu(198)

Question 6721: I am having trouble figuring out this problem. I know i should use the same base in all but do not know where each number should go, please help.
3( logb m-3logb n)
Click here to see answer by Mike(39)

Question 6738: I am having trouble finding the y intercept on this problem. I have come up with an answer but not sure if its correct.
Heres the problem...
2x - 5y = -10
Thank you for any help you can provide.
Click here to see answer by Earlsdon(6287)

Question 6871: f(x)= log x
I dont even know how to begin.
Click here to see answer by Mike(39)

Question 6958: 10^log1o^54need help with this question
Click here to see answer by longjonsilver(2297)

Question 7027: Help is this correct??
logbase3(3x-2)=2 I got x=11/3 is that right?
And... for this one solve the equation? logbase5(xsqrd+x+4)= 2 i got to xsqrd +x+4=5sqrd but i cant factor the xsqrd + x + 4 what do I do???
Thank you so much! I really appreciate it!
Click here to see answer by longjonsilver(2297)

Question 7024: I hope you can help me answer this question because I have no idea what I am supposed to do?!?!?!? The question is:
A teacher explained to her students that . One student said, "Therefore, the value of must be equal to -2." Is this correct reasoning? Justify your response.
Click here to see answer by longjonsilver(2297)

Question 7025: solve the equation
logbase3(3x-2)=2
I have absolutely no Idea what to do..can someone Please help me.
Thanks
Click here to see answer by prince_abubu(198)

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