Questions on Algebra: Logarithm answered by real tutors!

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Algebra: Logarithm

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Question 34528: Solve:
8^(4x-3)= 1/16, find the exact answer.
Click here to see answer by josmiceli(3003)

Question 34529: write out as sums and differences:
log base 5 (125x^5y^7/ cuberoot z^5) Simplify as much as possible..
I came up with log base 5 125 (possibly 3??) +log base 5 x^5 + 7 log base 5 y - 5 log base 5 z ^ 1/3..
All help is greatly appreciated
Click here to see answer by Prithwis(166)

Question 34699: I am having a problem solving this problem, #33 in Dr Rapalje's book, "Stepping through college algebra, one step at a time." log b (x-6)- log b (x)= log b (x-4). I have tried log b x-6 over x-4 = x, x-6 = x(x-4), x-6= x^2-4x, set to 0=x^2-4x-x+6, 0=x^2-5x+6, 0=(x-3) (x-2), x=3,x=2 is the answer I got, but it doesn't match the answer in the back of the book, which is 0, reject 3,2. Thank you.
Click here to see answer by stanbon(26252)

Question 34436:
Click here to see answer by Prithwis(166)

Question 34753: simplify
1/3[2ln(x+3) + lnx - ln(x2-1)]

Click here to see answer by mukhopadhyay(490)

Question 34875: 4. (25 pts) Write the logarithmic expression as a single logarithm and, if possible, simplify.
Show some work.
log 2 + log (x2 – 4) – log (5x – 10)
3. (25 pts) Write the given logarithm in terms of sums and/or differences of log x, log y, and log z. Show some work.
log(x2/y sqrt z)
I have spent the last 6 hours trying to figure these out and I have no idea of how to find the answer. I think getting started is the hardest part I am unsure of where to start. I have tried removing () by mutiplying by 2 then combining, but I still seem to have to many numbers to follow the quotient rule. If at all possible can you provide a descriptive explanation of this for me.
Thank you so much
Minta Mattocks

Click here to see answer by stanbon(26252)

Question 34919: in solving the equation log6(x-5)+log6(x-6)=1 a student correctly arrives at a step where x=8 or x=3. when these two values of x are verified?
a.neither
b.both
c.only x=3
d.only x=8
Click here to see answer by venugopalramana(3286)

Question 34920: the range of f(x)=log2x is ?
Click here to see answer by venugopalramana(3286)

Question 35061: I am frustrated and have i tried everthing but can't get it please help me.
The question is :- Solve 7^x = (3^(x+2))*(2^(x-3))
Thank you Darryl
Click here to see answer by venugopalramana(3286)

Question 35322: Please help me to solve this problem: 3 + lnX = 8
It would be greatly appreciated.
*Yasmin
Click here to see answer by narayaba(40)

Question 35274: In a town whose population is 2000, a disease creates an epidemic. The number of people (N) infected (t) days after the disease has begun is given by the function N(t)=2000/(1+19e^-0.6t) a. how many are initially infected with the disease (t=0)? b. how many infected after 2,5,8,12, and 16 days?
Click here to see answer by Nate(3495)

Question 35404: Hi! I need help with two problems. (^ means exponent follows)
2e^2x = 5^x+1
and...
log(x+1)-log(x)=2
thanks!
Click here to see answer by Nate(3495)

Question 35499: if, log2=a and log3=b, express log cuberoot972 in terms of a and b. the answer is 2a+5b over 3. please help.
Click here to see answer by rapaljer(3610)

Question 35550: can you please provide me an explanation of why the change of base formula can be proven. I need to provide proof why this works and I am having trouble finding the answer!!! Thank you for any help you provide.
Click here to see answer by stanbon(26252)

Question 35324: Please help me to solve this: 3e^-x - 4 = 9
thanks
*Triston
Click here to see answer by Nate(3495)

Question 35663: Solve the equation log^8(3x-1)=log^8(x+4).
Thank you!
Click here to see answer by rapaljer(3610)

Question 35678: Earthquake Magnitude Question:
If an earthquake in 1906 had an intensity of 8.27 on the Richter Scale & a 2nd quake in 1989 had a magnitude of 6.9, How many times greater was the magnitude of the 1906 quake than the 1989 quake?
I got 1.37 & I understand the intensity that if one quake is 7 & the other is 6 on the R.S. than the one that is 7 is 10 times as intenseas the one that is 6. So this one mentioned above is 10 times plus the .37 right? What is the correct answer? 10.37?
Click here to see answer by Earlsdon(4898)

Question 35732: how do you find the x and y intercepts of 2log(10x).
Click here to see answer by rapaljer(3610)

Question 35832: Solve: ln(3-y)-ln(2y+1)=ln(4y)
Click here to see answer by narayaba(40)

Question 35848: The number of years for $1800 to grow to $9400 at 8% quarterly?
A=P(1+r/m)^tm
9400 = 1800 (1 + 0.08/4)^4t
5.22 = (1 = 0.08/4) ^4t
I don't know how get the value of t from the equation
Could you please help me.
Click here to see answer by stanbon(26252)

Question 35882: Solve for x :log_2^x-_2 (x-1)=log_2^2 (log base 2 of x- log base 2 times x-1= log base 2 of 2)
One more please: expand:
log to the square root of x^5/ y^3
*Tonya
Click here to see answer by longjonsilver(2297)

Question 35902: I have this reveiw question and have been unsuccessful in finding help in my book. If you could help that would be FANTASTIC!
Question:
Rewrite the following as the logarithm of a single quantity:
log(x+2)- 3 logy + 2 logz
my thought was to change the base to each individual log function then solve, but that doesn't make sense.
Click here to see answer by venugopalramana(3286)

Question 36043: A kid's pond is stocked with 1200 trout. Four months later, about 400 remain. If the number N of trout remaining after T months is given by N=Ce^(kt), find the numbers C and k.
Click here to see answer by Nate(3495)

Question 36062: 3^(2x+1) = 5
Click here to see answer by Prithwis(166)

Question 36073: solve: log(6x)-log(x+1)=log4
Click here to see answer by Earlsdon(4898)

Question 36074: Find the dimensions of a rectangular box of 720 cubic inches of volume such that the wigth is three times as big as height and the length is 11in. more than the height.
Click here to see answer by qwe123a(7)

Question 36068: sketch the graph of the function and identify the vertical asymptote:
f(x)=log2(x-4)
Click here to see answer by stanbon(26252)

Question 36061: 3e^x - 1 = 6
Click here to see answer by stanbon(26252)

Question 36025: Please help! Thanks a million!!!
Solve the following for X:
1) log_6(2x)=log_6 (2)+log_6 (3x-4)
2) 2ln5=ln(4x-13)
3) log_4(3x+1)=2

Click here to see answer by stanbon(26252)

Question 36162: How do you graph a logarithmic function in easy-to-understand steps? I must be able to graph problems such as
y = log 1/3 (1/3 is the base of the logarithm) x-1 ... y = log1/3 x-1
y = log5 (5 is base of the logarithm) (x+2) ... y = log5 (x+2)
Why does one have parentheses and one doesn't? Does that make a difference? PLEASE HELP! ASAP! QUIZ TOMORROW AND I DON'T KNOW HOW TO GRAPH! THANKS!
Click here to see answer by stanbon(26252)

Question 36198: Write each expression in terms of sums, differences, and multiples of logarithms of the variables.
a)log base2 x^2 y^4/z^3 w^5
b)ln x^2 multiplied by the cube root of x+4
Click here to see answer by venugopalramana(3286)

Question 36197: Write each expression as a single logarithm.
a) 2log (base2) x - 4log (base2) y + 3log (base2)z
b) 1/2 ln(x+3)- 2ln3x
Click here to see answer by venugopalramana(3286)

Question 36435: I need to fill in the blanks of this sentence.
The graph of y= log x is the r.............. of the graph of y= 10^x in the line y=x. Such functions are called i........... of each other.
If you could help me I would greatly appreciate it. Thank you.
Click here to see answer by stanbon(26252)

Question 36427: The tension T on a cable varies directly as the cube of its surface S, and inversely as the square of its length L. If T=1 when S=2 and L=3, find T for S=4 and L=5/6..
Click here to see answer by stanbon(26252)

Question 35947: Can you please help me solve this problem? Solve for x: Log10(x-2)+log10(x+7)=1
This problem is from college algebra textbook chapter 3

This is what i have so far
log10(x-2)(x-7)=1
(x-2)(x-7)=10
x2-9x+14=10
Thank you
Click here to see answer by venugopalramana(3286)

Question 36557: use log5 2~0.4307 and log5 3~0.6826 to approximate the expression without a
calculator.
log5 18

I need some good examples so that I can figure the rest out for myself thanks abunch.
Click here to see answer by Nate(3495)

Question 36571: ok I have the factors of 12 but i dont know what to do with the 2/3 power.
log5 (12)^2/3
factors of 12 (2)(2)(3) I could figure out the rest but im not sure if the fraction is changed to a decimal or kept the same. i need to get this. I have finals next week and I really need some guidance. Thanks.

Click here to see answer by stanbon(26252)

Question 36554: solve the equation
3^x=500
Click here to see answer by rapaljer(3610)

Question 36717: Graph Log2(x+3)
Click here to see answer by josmiceli(3003)

Question 36786: I cannot solve this one...can someone please help me out?
Assume that the number of viruses present in a sample is modeled by the exponential function "f(t) = 10^t", where t is the elapsed time in minutes. How would you apply logarithms to determine when the sample will grow to 5 billion viruses?
Click here to see answer by stanbon(26252)

Question 36789: This on is very hard for me...
Write the logarithmic equation in exponential form. For example, the exponential form of "log5 25 = 2" is "5^2 = 25"

log 3 27 = 3
Click here to see answer by stanbon(26252)

Question 36793: I'm having trouble here:
onvert to logarithmic equations. For example, the logarithmic form of "23 = 8" is "log2 8 = 3".

16^(3/2) = 64
Click here to see answer by stanbon(26252)

Question 36788: I cannot see to solve this one. Can someone help me out? Thanks!
Maya has deposited $600 in an account that pays 5.64% interest, compounded continuously. How long will it take for her money to double?
Click here to see answer by Paul(988)

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