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 269857: This is more of a theoretical question:
When the logarithm is written as log(a)y = x. The "a" is called the base, but what is the x and y called? (Similarly, in y=a + bsin (x-c) + d, the "a" would be the amplitude, the "b" would be the period, ect).
Thank you very much!!
Click here to see answer by jim_thompson5910(35256)

Question 270248: 2 = 6x convert to logarithmic form
Click here to see answer by Alan3354(69443)

Question 270252: Convert the following equations into exponential form:
a. X = log54
b. 7 = log6Y
c. X= log8Y
d. 90 = log4Z

Click here to see answer by Alan3354(69443)

Question 270301: Solve for X, Y, and Z in the following systems of three equations using either substition or elimination methods:
a. X 2Y Z = 22
X Y = 15
3X Y Z = 37
b. 10X Y Z = 603
8X 2Y Z = 603
20X - 10Y - 2Z = -6
c. 22X 5Y 7Z = 12
10X 3Y 2Z = 5
9X 2Y 12Z = 14

Click here to see answer by jim_thompson5910(35256)

Question 270328: Cant seem to find my error while trying these questions???Please help
a. x2 * x4
b. z8/z12
c. log4y + log4z
d. log3y - log3z
I have to simplify the following expressions??

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

Question 270299: Solve for X and Y in the following problems using either substitution or elimination methods.
a. X Y= 10 , 3X Y = 12
b. 2X 5Y = 19 , 3X 3Y = 15
c. 4X Y = 22 , 2X 3Y = 16
d. 12X Y = 174 , 8X - 2Y = 36

Click here to see answer by Edwin McCravy(20060)

Question 270731: This life expectancy problem is really messing up when I try to solve it....
L(x)=79.25/(1+9.7135 * 10^24 * e^-.0304t)
* = multiply
^ = to the power of (ex: 5^7 Five to the seventh power)
Solve this equation when t=1970, and when t=1992.
I keep getting a weird decimal for t=1970, and somewhere around four thousand for t=1992. Can I have some help? Thanks!
Click here to see answer by Alan3354(69443)

Question 270831: how do i graph these logarithms funtions on word excel?
1.f(X)=2x+2 that is 2 raise to the power of x+x
2x-2
2.f(X)=3x
3x+1
3x-1 they are all raise to the power of x
3.f(X)=(1/2)X
(1/2)X +1
(1/2)X-1
Click here to see answer by solver91311(24713)

Question 270861: Please help me solve this problem.
Find y in the equation:
log2 64=y
Click here to see answer by papugai(18)

Question 270977: Please help; I have tried for 2 pages of work--
What is the approximate solution of 3 to the x+1 power = 5 to the x power?
Answer choices: a. 2.1507 b. 14l.4686 c. 0.4651 d. -0.4651
Thank you very much-Elizabeth
Click here to see answer by vleith(2983)

Question 270985: Solve 8^(x+8)=32^x
Click here to see answer by drk(1908)

Question 270985: Solve 8^(x+8)=32^x
Click here to see answer by Alan3354(69443)

Question 270946: I need help with this problem
log(3x+7)=0
Click here to see answer by ankor@dixie-net.com(22740)

Question 271286: A city is growing at the rate of 0.7% annually. If there were 4,913,000 residents in the ciyt in 1972, find how many(to the nearest ten-thousand) are living in the city in 2000.
Click here to see answer by checkley77(12844)

Question 271541: you deposit $200.00 in an that pays 7% interest compund yearly. Find the multiplier for the rate of exponential growth.
Click here to see answer by stanbon(75887)

Question 271486: what would be the smallest form of the x^16y^8/81 all in the fourth root?
Click here to see answer by ankor@dixie-net.com(22740)

Question 271546: Evaluate 4(5)^x for x= 3.2
Click here to see answer by stanbon(75887)

Question 271531: how do i reduce this: 3log base 5 of 2-(5log base 5 of x+log base 5 of 48) ? email address: dianasalerno0ooo@yahoo.com please show all steps so i can understand how to solve this problem. thank you.
Click here to see answer by ankor@dixie-net.com(22740)

Question 271879: 1.solve for x
log4 x^5=-1
2.solve for x in terms of k
log9 x + log9(x+9)=k
x=?
find x if k = 10

Click here to see answer by dabanfield(803)

Question 271884: hi
pls solve for x
1. log5 x+log5 (x+4)= log5(7)
2. (9/8)log5 x = 7
3. 5log4 x = -1
4. 5^(6x-7)= 9^(10x-6)
thank you
sonia
Click here to see answer by edjones(8007)

Question 272255: I am trying to solve this problem, and the answer is in the back of the book, but I keep getting the wrong answer. First for the problem: Tree Density:Ecologists studies the spacing between individual trees in a forest in Britsh Columbia. This lodgepole pine forest was 40 to 50 years old and had approximiately 1600 trees per acre that are randomly spaced. The probablity or liklihood that there is at least one tree located with a radius of x feet is estimated by P(x) =1-e^-0.1144x. For example, P(7)≈0.55 means that if a person picks a point at random in the forest, there is a 55% chance that at least one tree will be located within 7 feet.
a) Evaluate P(2) and P(20), and interpret the results.
b) Graph P. Explain verbally why it is logical for P to be an increasing function. Does the graph have a horizontal asymptote?
c) Solve P(x)=0.5 and interpret the results.
I keep getting the wrong answer. Here is what I came up with. I cannot figure out how to do the graphing part. I have the TI-Nspire, but outside of logs, I mostly use the TI-84 keypad. Here is my workup. 1 � e-0.1144x = 0.5

e-0.1144x = 0.5

ln(e-0.1144x) = ln(0.5)

-0.1144x = ln(0.5)

ln(0.5)
x = ---------- = 6.1
0.1144

I got that there is 0.5, or 50%, probability to find another tree in the circle with the radius 6.1 ft around. The actual answer in the back of the book . Here it is word for word.
a) P(2)≈0.20 and P(20) ≈ 0.90. There is a 20% chance that at least one tree is located within a circle having radius 2ft and a 90% chance for a circle having a radius 20 ft.
b) The larger the circle, the more likely it is to contain a tree. Y=1; probability cannot be greater than 1. They then show a graph with a window of [0, 25, 5] by [0, 1, 0]. But, I don�t know what to put in for Y1 or any others if needed.
c) x≈6.1. A circle of radius 6.1 ft has a 50-50 chance of containing at least one tree.
Thanks so much.
Click here to see answer by stanbon(75887)

Question 272291: The half-life of a certain radioatcive material is 85 days. An initial amount of the material has a mass of 801 kg. Write an exponential function that models the decay of this material remains after 10 days.
Click here to see answer by ankor@dixie-net.com(22740)

Question 272364: For which value of x is y=log x undefined?
Click here to see answer by Alan3354(69443)

Question 272494: The expression 1/2 logm - 3logn is equivalent to...
Click here to see answer by stanbon(75887)

Question 272700: how do i sumplify 6a^2b(-2a^2)^4
Click here to see answer by stanbon(75887)

Question 272864: 27^x =9^-x-1
Click here to see answer by Alan3354(69443)

Question 272865: log6(x+8)=log6 (x-4)+ 1/3log6 8
Click here to see answer by edjones(8007)

Question 272863: logX= -1.64
Click here to see answer by edjones(8007)

Question 272862: log7 X + log7 (x-6)=log7 27
Click here to see answer by edjones(8007)

Question 272924: I am trying to find an equation of the tangent line at the point indicated.
f (x) = log3 (8x + x-8), x = 1
Click here to see answer by Edwin McCravy(20060)

Question 273049: A local hamburger shop sold a combined total of 494 hamburgers and cheeseburgers on Friday. There were 56 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Friday?

Click here to see answer by stanbon(75887)

Question 273074: Simplify.
(u^4)^-7
Write your answer without using negative exponents.
Click here to see answer by stanbon(75887)

Question 273074: Simplify.
(u^4)^-7
Write your answer without using negative exponents.
Click here to see answer by josmiceli(19441)

Question 273501: Solve each Equation:
1. 8 � 3^x = �1
2. log(sub3)81 = x
3. log x � log 3 = 2

Evaluate the expressions. Round to the nearest hundredth.
4.log(sub5)2
5. log(sub2)5
Click here to see answer by edjones(8007)

Question 273621: find the logarithm of 1125
Click here to see answer by asuar010(338)

Question 273686: We are stumped on this problem:
Simplify. Leave in radical form: (cube root 5^2.7)/(cube root 5^4.5)
The answer is 1/(fifth root 5^3)
Any help showing the process would be much appreciated. Thank you!
Michelle and Cecil Jones
Click here to see answer by richwmiller(17219)

Question 273741: I am trying to solve this problem. I get how to do part A. I don�t know how to graph this. What do I put for Y1 and Y2 (if anything)? And on part C. How did it come to about 7 miles? I don�t understand where that comes from. The answer is in the back of the book. I have the TI-Nspire, but mostly use the TI-84 Silver Edition keypad.
The question is: Hurricanes are some of the largest storms on earth. They are very low pressure areas with diameters over 500 miles. The barometric air pressure in inches of mercury at a distance of x miles from the eye of a severe hurricane is modeled by the formula f(x) =0.48 ln (x+1) +27. It states
a) Evaluate f(0) and f(100).
b) Graph f in [0, 250, 1] by [25, 30, 1]
c) At what distance from the eye of the hurricane is the air pressure 28 Inches of mercury?
Thank you....
Click here to see answer by solver91311(24713)

Question 273795: If i had an equation to y=ab to the x, and it went to -1=(-3)b to the -1, what would b end up being??
Click here to see answer by jim_thompson5910(35256)

Question 274326: How do you work out the problem: logbase10(3m-5)+logbase10m=logbase102
Click here to see answer by edjones(8007)

Question 274430: how to solve each of these questions
a.) 2x=1/32
b.) 120x=25
c.) (4/9)^x= 81/16
thank you.......:)

Click here to see answer by stanbon(75887)

Question 274680: solve for x: log(base8)(2x+3) + log(base8)(x+1) = 1
Click here to see answer by nerdybill(7384)

Question 274677: find the inverses: F(x)= 3 * 5^x - 1 : G(x)= log(base5)(2x-7)
Click here to see answer by edjones(8007)

Question 274665: find all numbers "x" that satisfy the given condition: x^2 + 10x + 16 = e^3
Click here to see answer by edjones(8007)

Question 274779: Can someone please explain why logbx/ logby does not equal logbx - logby?
Click here to see answer by jim_thompson5910(35256)

Question 274916: how i do solve 2^x-1=1/64?
Click here to see answer by edjones(8007)

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