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

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 Algebra: Exponent and logarithm as functions of power Solvers Lessons Answers archive Quiz In Depth

 Question 464911: solve for x: 2^(2x) + 2^(x+2) - 12 = 0, I believe logarithms are needed. Click here to see answer by Alan3354(30993)

 Question 464917: Solve for x: 2^(2x) + 2^(x+2) - 12 = 0, I do believe logarithms are to be used to simplify. Click here to see answer by stanbon(57361)

 Question 465339: 1/square root 8 = 4^m-3 how do i solve this problem? the answer is m = 9/4 but im not sure how to get that answer Click here to see answer by stanbon(57361)
 Question 465339: 1/square root 8 = 4^m-3 how do i solve this problem? the answer is m = 9/4 but im not sure how to get that answer Click here to see answer by ewatrrr(10682)

 Question 465324: 14^x-3=21 i know the answer is approx 4.154 but im not sure how to correctly arrive at this answer. i would like to see the proper steps. Click here to see answer by ewatrrr(10682)

 Question 465391: give the logarithms of the following 1. log 1000 2. 3.20 Click here to see answer by stanbon(57361)

 Question 465400: my last problem stated this "if interest is compounded annually, how much is 1000 worth in 8 years at 8%" and my answer was %1850.93...so i think you need that info to answer problems 1 and 2! thanks so much! the formula to find the total amount in your savings account(if interest is compounded continuously) after t years is A=Pe^rt (A=total amount, P=original amount, and r=interest rate.) 1. how long does it take your money to double at 8% interest? (round to the nearest year.) 2. what about at 5%? (round to the nearest year.) Click here to see answer by stanbon(57361)

 Question 465419: 7-3 Click here to see answer by richard1234(5390)

 Question 465420: (-5)-3 Click here to see answer by stanbon(57361)

 Question 465421: 7-3 Click here to see answer by Alan3354(30993)

 Question 465367: give the logarithms of the following. 1. log 1000 2. log 3.20 3. log(1000)^1/2 <--- thats the whole exponent the 1/2 Click here to see answer by Alan3354(30993)

 Question 465496: I need help with logs log3(x+1)=log3 6 is it like x+1/3 = ln6/ln3 Click here to see answer by Alan3354(30993)

 Question 464822: f(x) = 3x Find f(2) The x is the exponent of 3. So I have y = B of x. right? 2 = 3x and this is where i get lost. Thanks Chris Click here to see answer by sofiyac(695)

 Question 466217: Section 5.3 #96. Atmospheric Pressure The atmospheric pressure p on a balloon or plane decreases with increasing height. This pressure, measured in millimeters of mercury, is related to the height h(in kilometers) above sea level by the function p(h) = 760e–0.145h (a) Find the atmospheric pressure at a height of 2 kilometers (over a mile). (b) What is it at a height of 10 kilometers (over 30,000 feet)? Click here to see answer by stanbon(57361)

 Question 466125: I just don't get this log32 (x) + log(2x)=1 Solve for x Click here to see answer by stanbon(57361)

 Question 466677: Can Someone please help me with this question The revenue, R, generated by selling games with a particular price is given by R(p) = –15p2 + 300 p + 1200. Graph the revenue function without a calculator and find the price that will yield the maximum revenue. What is the maximum revenue? Explain in real world terms why this graph is parabolic. Click here to see answer by ccs2011(207)

 Question 466761: write 15^2=x in logarithmic form Click here to see answer by Alan3354(30993)

 Question 466943: How do I write these as the logarithm of a single expression... log(x^2+3x-10)-log(x+5) 3log(2x^2)-(1/2)log(16x^4) -2log(P)+(1/3)log(R) Click here to see answer by Big Poop(157)

 Question 467119: How do I write these as the logarithm of a single expression... log(x^2+3x-10)-log(x+5) 3log(2x^2)-(1/2)log(16x^4) -2log(P)+(1/3)log(R) Click here to see answer by stanbon(57361)

 Question 467175: need help fast please A data processing consultant charges clients by the hour. His weekly earnings E are modeled by the function E=0.2x^2+40x where x is his hourly rate in dollars. Can he earn \$2500 in a single week? Explain. Click here to see answer by Big Poop(157)
 Question 467175: need help fast please A data processing consultant charges clients by the hour. His weekly earnings E are modeled by the function E=0.2x^2+40x where x is his hourly rate in dollars. Can he earn \$2500 in a single week? Explain. Click here to see answer by robertb(4012)

 Question 467233: Can someone please help with this problem In 1965 the federal debt of the United States was \$3.22.3 billion. During the next 30 years, the debt in creased by about 10.2% each year. Write a model giving the amount (D) (in billions of dollars) of debt (t) years after 1965. About how much was the federal debt in 1980? Graph he model Click here to see answer by Big Poop(157)

 Question 467232: Can someone please help with this problem In 1965 the federal debt of the United States was \$3.22.3 billion. During the next 30 years, the debt in creased by 10.2% each year. Write a model giving the amount (D) (in billions of dollars) of debt (t) years after 1965. About how much was the federal debt in 1980? Graph he model Click here to see answer by Big Poop(157)

 Question 467322: 1. Identify the equation that represents the function in the following graph. 1. y = (1/2)x 2. y = (1/2)(x + 1) 3. y = 2x 4. y = 2(x – 1) 2. Solve the equation 3x = 3(3x + 1). 1. 1/3 2. –1/3 3. 1/2 4. –1/2 3. Solve the equation 2(2x – 1) = 8(x + 7). 1. –22 2. 22 3. –8 4. 8 4. Solve the equation (1/3)x = 3(x – 6). 1. –3 2. 0 3. 3 4. undefined 5. Write the equation 73 = 343 in logarithmic form. 1. log3 343 = 7 2. log7 343 = 3 3. log3 7 = 343 4. log7 3 = 343 6. Write the equation log6 (1/36) = –2 in exponential form. 1. –2(1/36) = 6 2. (1/36)(–2) = 6 3. 6–2 = 1/36 4. –26 = 1/36 7. Evaluate the expression log12 122. 1. 0 2. 1 3. –1 4. 2 8. Solve the equation logb 9 = 2. 1. 0 2. 3 3. 6 4. 7 9. Solve the equation log3 (3x – 6) = log3 (2x + 1). 1. –1 2. 1 3. 3 4. 7 10. Evaluate the expression 10(log 12 – log 4). 1. 2 2. 3 3. 4 4. 8 11. Solve the equation log3 14 + log3 x = log3 42. 1. 3 2. 11 3. 20 4. 28 12. Solve the equation 3log5 x – log5 4 = log5 16. 1. 4 2. 8 3. 12 4. 16 13. Solve the equation (1/3)log7 64 + (1/2)log7 121 = log7 x. 1. 7 2. 15 3. 19 4. 44 14. Find log2 15 given that log2 5 = 2.322 and log2 3 = 1.585. 1. .737 2. 1.465 3. 3.680 4. 3.907 15. Find log3 25 given that log3 5 = 1.465. 1. 2.930 2. 2.146 3. 1.398 4. not enough information 16. If log .5 = –.3010, what is the mantissa of log .5? 1. 0 2. 1 3. .3010 4. .6990 17. If log 50 = 1.6990, what is the characteristic of log 50? 1. 0 2. 1 3. .3010 4. .6990 18. Find the logarithm of 1500. Round the answer to four decimal places. 1. 3.1761 2. .1761 3. .1761 – 3 4. 1761 19. Find the antilogarithm of 3. Round the answer to four decimal places. 1. 20.0855 2. 1.0986 3. .4771 4. 1000 20. Evaluate the expression ln 2.5. Round the answer to four decimal places. 1. .3987 2. .9163 3. 12.1825 4. 316.2278 21. Solve the equation 100e .75x = 500. Round the answer to four decimal places. 1. 2.1458 2. 3.1266 3. 4.2134 4. 5.5945 22. Evaluate the expression ln e. 1. .9933 2. 1 3. 10 4. 100 23. Solve the equation 6x = 72. Round the answer to four decimal places. 1. 1.0792 2. 2.1325 3. 2.2146 4. 2.3869 24. Solve the equation 6(3x + 1) = 8. Round the answer to four decimal places. 1. .0021 2. .0535 3. .0721 4. .0839 25. Solve the equation 7^(x – 2) = 5x. Round the answer to four decimal places. 1. 8.3219 2. 9.6253 3. 10.1263 4. 11.5665 Click here to see answer by Alan3354(30993)

 Question 467335: Compute by using logarithms. ^4√6 Click here to see answer by Alan3354(30993)

 Question 467358: how do you solve (2x^2)^3*(1/2x)^2? Click here to see answer by MathLover1(6634)

 Question 467359: how do you solve (-y)^3*(2y^2)? Click here to see answer by jim_thompson5910(28595)

 Question 467590: Can someone please help with this Use the change of base formula to write two equations that are equivalent to y = log[2]x Click here to see answer by Alan3354(30993)

 Question 467651: x^2+16x+63=0 Solve the quadratic equation by completing the square. Click here to see answer by jorel1380(2518)

 Question 467765: how do i find 5 ^ SQRT OF 3 USING A SCINTIFIC CALCULATOR' Click here to see answer by Alan3354(30993)

 Question 468302: Solve the equation log 3x+5=3 Click here to see answer by ewatrrr(10682)

 Question 468306: Suppose you invest \$130 at 4% compounded continuously. a. Write an exponential function to model the amount in your investment account. b. Explain what each value in the function model represents. c. In how many years will the total reach \$600? Show your work. Click here to see answer by ewatrrr(10682)
 Question 468306: Suppose you invest \$130 at 4% compounded continuously. a. Write an exponential function to model the amount in your investment account. b. Explain what each value in the function model represents. c. In how many years will the total reach \$600? Show your work. Click here to see answer by Gogonati(809)

 Question 468317: Does y=11(8/13)^x represents exponential growth or exponential decay. Click here to see answer by ccs2011(207)

 Question 468355: how do I Divide using long division. 2x^3-29x+12/ x+4 Click here to see answer by ewatrrr(10682)

 Question 468366: Write the equation in its equivalent logarithmic form. 7^2 = 49 Click here to see answer by Alan3354(30993)

 Question 468368: how can I evaluate this expression log51 Click here to see answer by Alan3354(30993)

 Question 468360: Solve the problem. Solve the equation 2x3 - 23x2 + 71x - 30 = 0 given that 5 is a zero of f(x)= 2x^3- 23x^2 = 71x- 30 . Click here to see answer by ewatrrr(10682)

 Question 468363: Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) = x3 + 5x2 + 6x + 2 Click here to see answer by ewatrrr(10682)

 Question 468305: The half-life of a radioactive substance is the time it takes for half of the substance to decay. The half-life of carbon-14 is 5700 years. a. Write an exponential function to model the decay of a 470-mg sample. b. Explain what each value in the function model represents. c. To the nearest hundredth, find the amount of carbon-14 remaining after 2619 years. Explain how you found this amount. Click here to see answer by ankor@dixie-net.com(15656)

 Question 468458: rewrite using positive exponents (6xy)-4/5 Click here to see answer by MathLover1(6634)

 Question 468456: find lim[x:3/2]2x^2-9x-18/2x-3 Click here to see answer by Tatiana_Stebko(1326)

 Question 468588: Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 10x = 3.76 Click here to see answer by rfer(12662)

 Question 468590: Use properties of logarithms to condense the logarithmic expression. ln x + 8ln y Click here to see answer by nerdybill(6962)

 Question 468592: Use properties of logarithms to expand the logarithmic expression as much as possible. logb (yz5) Click here to see answer by nerdybill(6962)

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