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 1141525: How do you write this expression as a single logaritm
3 log 2+5 x-2 log y
Click here to see answer by josgarithmetic(39620)

Question 1141650: Verify the following identity by using an angle sum identity: cos (2x) = 1 - 2(sin2 x). Hint (2x = x + x)
Click here to see answer by ikleyn(52800)

Question 1141648: If the terminal side of a 330 degree angle intersects a unit circle, what would the coordinates at the point of intersection?
Click here to see answer by Alan3354(69443)

Question 1141649: Solve for x: 3 + cos 2x = 7/2; only include answers on [0, 2π]
Click here to see answer by josmiceli(19441)

Question 1141649: Solve for x: 3 + cos 2x = 7/2; only include answers on [0, 2π]
Click here to see answer by Alan3354(69443)

Question 1141947: You have a piggy bank containing a total of 56 coins in dimes and quarters. If the piggy bank contains $9.35, how many dimes are there in the piggy bank?
Click here to see answer by Alan3354(69443)

Question 1141945: The sum of two numbers is 134. The second number is
16 less than twice the first number. Find the numbers.
Click here to see answer by ikleyn(52800)

Question 1142542: Simplify: √(2^(x+2)) + 5 × √5(2x) - 9 = √(3)2^(x+2) + 21
Click here to see answer by greenestamps(13200)

Question 1142651: Suppose the functions f, g, h, r and l are defined as follows:
f (x) = 3 log3 x + log 1/3x
Write down Df and solve the equation f (x) = − log3 1/4

Click here to see answer by Alan3354(69443)

Question 1143374: Suppose the functions f,g,h,r and l are defined as follows:
f(x)=3log^3X+log 1/3 x

write down Df and solve the equation f(x)=-log3 1/4
Click here to see answer by greenestamps(13200)

Question 1143544: Consider the growth of the following virus. A new virus has been created and is distributed to 100 computers in a company via a corporate email. From these workstations the virus continues to spread. Let t=0 be the time of the first 100 infections, and t=17 minutes the population of infected computers grows to 200. Assume the anti-virus to grow exponentially.
What will the population of the infected computers be after 1 hour ?
What will the population be after 1 hour and 30 minutes?
What will the population be after a full 24 hours ?

Click here to see answer by greenestamps(13200)

Question 1143609: Please kindly help with this questions.
solve e^(2x+1) + 9e^x - 11 = 0

Click here to see answer by ikleyn(52800)

Question 1143610: Please kindly help with this question. Many thanks.
Given log C (base a) - log x (base a) = 5/3, express x in terms of a and N.
Click here to see answer by greenestamps(13200)

Question 1143674: The half-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only
76% of the carbon-14 expected in living matter, when did the tree die?
Click here to see answer by ikleyn(52800)

Question 1143691: I got stuck while solving this question:
A quantity N is decreasing such that at time t, N = Noexp(-yt), where No is the amount at t = 0 and y = 0.5. Find the value of t when N = No/5.
Click here to see answer by greenestamps(13200)

Question 1143776: If log base b of 2 =x and log base b of 3 = y, evaluate the following terms of x and y:
A) log base b of 36
B) log base b of 432
C) log base b of 3 (all over)
log base b of 4
Click here to see answer by ikleyn(52800)

Question 1144225: ln(7-p)=ln(-5p-1)
Click here to see answer by Theo(13342)

Question 1144616: Please help me solve this problem. "A researcher is investigating a specimen of bacteria. She finds that the original 1,000 bacteria grew to 2,084,000 in 60 hours. How fast does the bacteria (a) double? (b) quadruple?". Please kindly explain to me how. Thank you in advance.
Click here to see answer by Alan3354(69443)

Question 1144946: sqrt(x)^sqrt(x)^sqrt(x) = 2^512 Find x.
Is there a way to do this without using the logarithm function?
Click here to see answer by Edwin McCravy(20059)

Question 1145007: Solve by integration
Click here to see answer by Edwin McCravy(20059)

Question 1145219: Given that 6log(n+4)=2log8,find n

Click here to see answer by Alan3354(69443)

Question 1145389: find the area bounded by the parametric equations at interval 0 ≤ t ≤ 2π.
Click here to see answer by greenestamps(13200)

Question 1145388: find the constant term in the expansion of (x^2-1/x)^9
Click here to see answer by greenestamps(13200)

Question 1145473: Find the domain and range of the function f(x)=-e^-x+8
Click here to see answer by Theo(13342)

Question 1145474: Find an exponential function of the form f(x)=ba^-x+c that has the given horizontal asymptote and x and y-intercepts. y =-13; y-intercept 624; x-intercept 2
Click here to see answer by MathLover1(20850)

Question 1145749: Calculate the value of x where the function
y=f(x)=1,822.8×(1.4^x )
This will predict the transistor value f(x)=406,500,000,000.

Final answer (x)
Round off the final answer to the nearest whole value.

What is the exact year?

Show your work below using Equation Editor:

I tried to calculate the value of x function: y = f(x) = 1,822.8 x (1.4x) and I tried to solve for x, and I got 2 = |3x|
|2y| + 3 = 2 + 3
-2 (y+2) = 2 - y
I'm not sure if this is correct, so I wanted to know if I could have a second opinion on this.
Click here to see answer by ikleyn(52800)

Question 1146473: what is the coefficient of x^2y^4 in the expansion of
Click here to see answer by richwmiller(17219)

Question 1146472: what is the coefficient of x^7 y in the expansion of (3x-4y)^8
Click here to see answer by greenestamps(13200)

Question 1146618: principal of $3500
is invested at 5.75%
interest, compounded annually. How many years will it take to accumulate $5000
or more in the account?
Click here to see answer by greenestamps(13200)

Question 1146776: is 1 + sqrt(-x-2) a one-to-one function?
Click here to see answer by Theo(13342)

Question 1147085: The present age of Jacob’s father is three times that of Jacob. After 5 years, sum of their ages would be 70 years. Find their present ages.
Click here to see answer by josgarithmetic(39620)

Question 1147151: two taxi cabs leave in the terminal at the same time. one taxi travels south at 30 mph. and the other taxi travels north at 40 mph. how long will it take until the two taxi are 75 miles apart?
Click here to see answer by josgarithmetic(39620)

Question 1147645: Hi The other day I came up with the following equation and
I am absolutely stumped as to how to solve it.
2 raised to the X power =6X
I used a graphing calculator
which gave me two solutions:
X=0.19 or X=4.88 (approximately)
But I have no idea how to use
Algebta/Logs to solve for X.

I was wondering if you could help.
Thanks
Jim S

Click here to see answer by Alan3354(69443)

Question 1147840: How are you? I really need help.
e^x^2=e^9x*1/e^x
Click here to see answer by Alan3354(69443)

Question 1147910: I've been trying to answer this question but I don't know how to find b and how to proceed from there.
U.S. Population

YEAR POPULATION
1930 122,800,000
1940 131,700,000
1950 150,700,000
1960 179,300,000

It is estimated that the limiting population that the United States can support is 500,000,000 people. Predict the population for the year 2000 using the logistic growth model on the basis of the data in the years 1940 and 1950. In other words:

* Let P = P (t) be the population, where t is the number of years after 1940.
* Assume P (t) is of the form given by the logistic equation. Determine what the value of L must be in this case.
* Find the exact values of P (0) and P (10) from the U.S. Population table given above. Use these two data points to find the values of b and k in the formula for P (t).
Answer to the nearest 1 million people
Click here to see answer by greenestamps(13200)

Question 1147955: A drug is eliminated from the body through urine. Suppose that for a dose of 10 milligrams, the amount A(t) remaining in the body t hours later is given by
A(t) = 10(0.7)t and that in order for the drug to be effective, at least 2 milligrams must be in the body.
(a) Determine when 2 milligrams are left in the body. (Round your answer to two decimal places.)
(b) What is the half-life of the drug? (Round your answer to two decimal places.)
Click here to see answer by josgarithmetic(39620)

Question 1147954: Suppose $500 is invested at a rate of 11% per year compounded monthly. (Round your answers to the nearest cent.)
(a) Find the principal after 1 month.
(b) Find the principal after 6 months.
(c) Find the principal after 1 year.
(d) Find the principal after 20 years.
Click here to see answer by ikleyn(52800)

Question 1147952: The number of bacteria in a certain culture increased from 500 to 1000 between 7:00 A.M. and 9:00 A.M. Assuming growth is exponential, the number f(t) of bacteria t hours after 7:00 A.M. is given by f(t) = 500(2)t/2.
Estimate the number of bacteria in the culture at 8:00 A.M., 10:00 A.M., and 11:00 A.M. (Round your answers to the nearest whole number.)

Click here to see answer by greenestamps(13200)

Question 1148013: The length (in centimeters) of many common commercial fish t years old can be approximated by a von Bertalanffy growth function having an equation of the form
f(t) = a[1 − be^−(kt)], where a, b, and k are constants.
(a) For Pacific halibut, a = 200, b = 0.956, and k = 0.18. Estimate the length of a 13-year-old halibut.

(b) Use the graph of f to estimate the maximum attainable length of the Pacific halibut.
cm
Click here to see answer by ikleyn(52800)

Question 1148014: The radioactive tracer ⁵¹Cr can be used to locate the position of the placenta in a pregnant woman. Often the tracer must be ordered from a medical laboratory. If A₀ units (microcuries) are shipped, then because of the radioactive decay, the number of units A(t) present after t days is given by
A(t) = A₀e^(−0.0249t)
a) If 40 units are shipped and it takes 2 days for the tracer to arrive, approximately how many units will be available for the test? (Round your answer to one decimal place.)
units
(b) If 40 units are needed for the test, approximately how many units should be shipped?
Click here to see answer by Theo(13342)

Question 1148015: A schematic of a simple electrical circuit consisting of a resistor and an inductor is shown in the figure. The current I at time t is given by the formula
I = 25e^(−Rt/L), where R is the resistance and L is the inductance. Solve this equation for t.

Click here to see answer by Alan3354(69443)

Question 1148012: Solve the equation.
16^(8x) · (1/4)^(3x + 8)= 64 · (4x)^−6
Click here to see answer by greenestamps(13200)

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