Questions on Algebra: Exponent and logarithm as functions of power answered by real tutors!

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Question 1183438: find the values of the following without using calculators.
(a)log x^3 / log cube root x where (x is not 1)
I know the answer for this question, but I'm not sure my way of doing it is right. Therefore I need someone nice to help me check.
ok after doing some stuff I ended up with log x cube divide by log x to the power of a fraction 1/3. To get 9 the answer I simply "cancel out" the "common factor" log x and proceed with 3/1/3 (as a fraction) = 9
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Question 1183570: • What leads many observers to assume
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Question 1183584: f(x)= -x-2
find f(-3)
f(-3)=Why is -(-3)-2
=f(-3)= 3-2
f(-3)= 1
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Question 1183840: Solve for x if 3^x=9x

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Question 1183840: Solve for x if 3^x=9x

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Question 1183868: Four people can eat 2 bags of food each weighing 20 kg in 24 days. How many people can eat 6 bags of food of the same weight in 36 days?.
Click here to see answer by josgarithmetic(39620)

Question 1184015: You bought a car to the value of R100 000 five years ago. Its value has been decreasing by 14% per year. Draw the graph showing this decrease (round off to the nearest R1000)

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Question 1184032: Please help me solve
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Question 1184032: Please help me solve
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Question 1184360: 10log(I/10^-12)=129

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Question 1184360: 10log(I/10^-12)=129

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Question 1184515: In working for 10 hours a day , 12 men can do a certain piece of work in 6 days.For how many hours a day must 20 men work in order to do the same amount of work in 14 days?
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Question 1184514: Find the total amount of money received if Tshs 800000 is deposited in a bank at the rate of 9% compounded semi annually in one year
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Question 1184577: 28p^5q^3/ 40p^3q^5
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Question 1184771: (2,3)

y < 2x² - 3x + 1
True or False?
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Question 1185179: -4(3x+2)^2 how do I combine and simplify?
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Question 1185267: How does the graph of y=-2(1/3)^x-2 compare to the graph of the parent function y=b^x? Consider describing transformation in your comparison.
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Question 1185656: Log (30/16)_2 log (5/9+log(400/243)
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Question 1185912: A company begins a radio advertising campaign in New York City to market a new CD-ROM video game. The percentage of the target market that buys a game is given by the function f(t)=100(1-e^-0.05t), where T is the number of days of the campaign and f(t) is a percent. Find the percentage of the target market that buys a game after a 10 day campaign
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Question 1185929: Solve 3 raise tothe power 2x=81
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Question 1186377: You take out Php 20,000 loan at a 5% interest rate compounded annually.
How much will you owe after 10 years?

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Question 1186865: Solve the following exponential equation. Express your answer as both an exact expression and a decimal approximation rounded to two decimal places.
3e^−x+11 = 48
If you wish to enter log or ln, you must use the keypad

x = __________________ ≈ _________
Click here to see answer by Theo(13342)

Question 1187206: the dimension of rectangular metal box are 3cm 5cm and 8 cm. if the first 2 dimension are increased by the same numbers of centimeters, while the 3rd dimension remains the same, the new volume is 34cmcube more than the original volume. what is the new dimension of the enlarged rectangular metal box?

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Question 1187524: EColi culture doubles every 40 minutes. If 30 EColi are present initially, what will the number of EColi be after 3 hours?
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Question 1187531: The half-life of a radioactive material is the time in which half of it will disintegrate. If its amount after t years is , what is its half life?
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Question 1187528: A research person made 160 mg of radioactive sodium and found that there was only 20 mg left 45 hours later. what is the half life of radioactive sodium?
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Question 1187573: the half life of caffeine in a child's system when a child eats or drinks something with caffeine in it is 2.5 h How much caffeine would remain in a child's body if the child ate a chocolate bar with 20 mg of caffeine 8 hours before?
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Question 1187575: A radioactive form of uranium has a half life of 2.5x 10^5 years. a) Find the remaining mass of 1 g sample after t years
b) Determine the remaining mass of this sample after 5000 years.
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Question 1187692: write the exponential function through (a,b) and (a+1, b/3)
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Question 1187770: The rate of increase in the population of a certain kind of bacteria is proportional to the
population at any time. If in the last eight years, the population increased from 50000
to 120000, what will be the population of bacteria 16 years from now?
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Question 1187771: The half life of a sodium is 15 hours. How long does it take for 95% of a sample of this
isotope to decay?
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Question 1187926: Find f’(t) for f(x) = (3x-4) (4x^3 - x^2 + 1)

Find f’(t) for f(x) = x/(4x-6)

Find the derivative of the function f(x) = (2x-7)/(3x-2) at x = 2.

Find f’(x) for f(x) = (x^2 + 2)^3

Find dy/dx for y=ln⁡(3x^3-x^2)

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Question 1187924: 8. Let C(x) be the cost function and R(x) the revenue function. Compute the marginal cost, marginal revenue, and the marginal profit functions.
C(x) = 0.0005x^3 - 0.012x^2 + 100x + 30,000
R(x) = 450x

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Question 1187923: 1. Suppose that the total profit in hundreds of dollars from selling x items is given by P(x) = 4x^2 - 5x + 10. Find the marginal profit at x = 5.
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Question 1187925: 9. The total profit from selling x units of doorknobs is P(x) = (6x - 7) (9x - 8). Find the marginal average profit function.
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Question 1187921: 2. Suppose an object moves along the y-axis so that its location is y = f(x) = x^2 + x at time x (y is in meters and x is in seconds). Find the average velocity (the average rate of change of y with respect to x) for x changing from 2 to 9 seconds.
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Question 1187972: Find f’(t) for f(x) = x/(4x-6)
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Question 1187972: Find f’(t) for f(x) = x/(4x-6)
Click here to see answer by Alan3354(69443)

Question 1187970: 8. Let C(x) be the cost function and R(x) the revenue function. Compute the marginal cost, marginal revenue, and the marginal profit functions.
C(x) = 0.0005x^3 - 0.012x^2 + 100x + 30,000
R(x) = 450x

Click here to see answer by Solver92311(821)

Question 1187971: 11. Find f’(t) for f(x) = (3x-4) (4x3 - x2 + 1)
Click here to see answer by Alan3354(69443)

Question 1187969: 7. Suppose that the total profit in hundreds of dollars from selling x items is given by P(x) = 4x^2 - 5x + 10. Find the marginal profit at x = 5. show working.
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