# 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 373938: The bases on each side of the equation cannot be made the same. Therefore, take the logarithm of each side in order to solve the equation. log4 8 Click here to see answer by Earlsdon(6287)

 Question 373931: Solve the equation by making the bases the same on each side of the equation 5^x=1/125 Click here to see answer by Earlsdon(6287)

 Question 374179: A radioactive substance decats by 5% every hour. Intially rhere are 500g of substance. a. How many grams remain after 6 hours? b. What is the half life substance? c. How long will it take the 500g to decay to 200g? Click here to see answer by robertb(4012)

 Question 374584: Find the inverse of the logarithmic function f(x)=-ln(x-2). Steps I've done so far: 1. f(x)=-ln(x-2) 2. y=-ln(x-2) 3. x=-ln(y-2) What is the next step? I am not sure what to do with -ln. My instructor said the answer is: y=e^-x+2 but I don't know how he gets the -x. I know ln also stands for e. y=-e^x+2 makes more sense to me. Click here to see answer by robertb(4012)

 Question 374505: List the transformations, in order, for the following function: f(x)=4-3^x-1 The first thing I did was rewrite the function: f(x)=-3^(x-1)+4 - Horizontally shifts 1 unit to the right (because of (x-1)) - Reflects about the x-axis (because of the negative in front of the 3) - Vertically shifts 4 units up (because of the +4) Is this correct? Does the function vertically stretch by a factor of 3? In my notes a compress/stretch is said to be: a > 1 then vertically stretches by factor of a 0 < a < 1 vertically compresses by factor of a But the instructor walked us through this problem but did not mention anything about a vertical stretch or compression. Click here to see answer by jsmallt9(3296)

 Question 375399: write an exponential equation y=ab^x whose graph passes through these points (1,10), (2,25) Click here to see answer by nerdybill(6948)

 Question 375414: Express as equivalent expression that a single logarithm and if possible, simplify. (not sure how to subscript the 'a') Click here to see answer by nerdybill(6948)

 Question 375439: I'm not really sure how to remove the coefficients in the following problem: 2*log2(x) - log2(10) = 3*log2(4) Click here to see answer by Earlsdon(6287)
 Question 375439: I'm not really sure how to remove the coefficients in the following problem: 2*log2(x) - log2(10) = 3*log2(4) Click here to see answer by ewatrrr(10682)

 Question 375415: express as equivalent expression that a single logarithm and if possible simplify ('a' should be in subscript) loga(2x+1-)-loga(x^2-25) Click here to see answer by Fombitz(13828)

 Question 375848: Explain the differences between solving these two equations: • log3(x - 1) = 4 and log3(x - 1) = log34 Click here to see answer by ewatrrr(10682)

 Question 375847: for all non zero r,t,z values 12r5tz7 / -4rt5z3 =? please note that the numbers 5, 7, 5, and 3 are exponents to the letters Click here to see answer by Fombitz(13828)

 Question 375927: I need to find a solution (x,y) for the following set of numbers.... y=logbase2(x+1) y=5-logbase2(x-3) I dont know how to solve this one.... Click here to see answer by Alan3354(30924)

 Question 375924: I need to find a solution (x,y) for the following set of numbers.... y=e^(4x) y=e^(2x)+6 I found x to be ln6/2 but i am not sure if that is right.... Click here to see answer by user_dude2008(1861)

 Question 375947: Determine the constants N(o) and K so that the graph y=N(o)e^(kt) passes through the points (2,3) and (8,24). I dont even know how to start this problem... any help would be greatly appreciated!! Click here to see answer by robertb(4012)
 Question 375947: Determine the constants N(o) and K so that the graph y=N(o)e^(kt) passes through the points (2,3) and (8,24). I dont even know how to start this problem... any help would be greatly appreciated!! Click here to see answer by user_dude2008(1861)

 Question 375929: Find the points where y=-2x-2 intersects with parabola y=.5x^2 Click here to see answer by mananth(12269)

 Question 375899: I am so appreciated for helping me out these questions: 1.(x-2)(x+3)^2 OVER x^4-13x^2+36. 2. If polynomial p(x)=2x^3 -3x^2-10 has exactly one real zero r, where -1<=r<=1, which following is true: A. -1 3. Which shows a portion of graph of y= y|-|-x|| ? 4. what is x if 3x^2-2+7=0 then (x- 1/3)^2= ? 5. If y=b^x and b>1, which one is true: A log y b=x. B. log b x=y. C. another answer 6. the radian measure of angle containing x degree is: A.Pi x/180 B. Pi x/ 180. C. other answer 7.If f(x)= x^2, when x>0 and c>1, then f(x^c)= ? 8 2log10x-log10y=? 9.for x#0, if f(x)3x^2 and g(x)=1/2, then f(g(x))= ? 10 3+i/2-i = ? 11. if cotx^0=1, then x=? 12. y=x+1 and xy=2 so what x? 14. If f(x)=3-2x and f^-1 denotes the inverse of f, then f^-1(o) is ? 15. what is the solution set of 2sin^2(x)-3sin(x)-2=0 where 0<=x<=2pi Click here to see answer by Fombitz(13828)

 Question 375897: I am so appreciated for helping me out these questions: 1.(x-2)(x+3)^2 OVER x^4-13x^2+36. 2. If polynomial p(x)=2x^3 -3x^2-10 has exactly one real zero r, where -1<=r<=1, which following is true: A. -1 3. Which shows a portion of graph of y= y|-|-x|| ? 4. what is x if 3x^2-2+7=0 then (x- 1/3)^2= ? 5. If y=b^x and b>1, which one is true: A log y b=x. B. log b x=y. C. another answer 6. the radian measure of angle containing x degree is: A.Pi x/180 B. Pi x/ 180. C. other answer 7.If f(x)= x^2, when x>0 and c>1, then f(x^c)= ? 8 2log10x-log10y=? 9.for x#0, if f(x)3x^2 and g(x)=1/2, then f(g(x))= ? 10 3+i/2-i = ? 11. if cotx^0=1, then x=? 12. y=x+1 and xy=2 so what x? 13. where defined tanx=? 14. If f(x)=3-2x and f^-1 denotes the inverse of f, then f^-1(o) is ? Click here to see answer by Fombitz(13828)

 Question 376127: How do you simplify (-3x) to the power of -2 using only positive exponents? What is the slope of y=5/2? How do you simplify with only positive exponents.... p to the power of 2 over p to the power of 6? Click here to see answer by Fombitz(13828)

 Question 376074: Pls help! If you can answer either one of them, I am so appreciated. 1.(x-2)(x+3)^2 / x^4-13x^2+36. 2. If polynomial p(x)=2x^3 -3x^2-10 has exactly one real zero r, -1<=r<=1, which following is true: A. -1<0 B. 0<1 or C.other answer? 3. what is a portion of graph of y= y|-|-x|| ? graph it. 4. what's X if 3x^2-2+7=0 then (x- 1/3)^2= ? 5. If y=b^x and b>1, which one is true: A log y b=x. B. log b x=y. C. other answer. 6. The radian measure of angle containing x degree is: A.Pi x/180 B. Pi x/ 180. C. other answer 7.If f(x)= x^2, when x>0 and c>1, then f(x^c)= ? 8 2log10x-log10y=? 9.for X# 0, if f(x)3x^2 and g(x)=1/2, then f(g(x))= ? 10 3+i/2-i = ? 11. If cotx^0=1, then x=? 12. Y=x+1 and x.y=2 so what x? 13. where can you defined tan X=? 14. If f(x)=3-2x and f^-1 denotes the inverse of f, then f^-1(o) is ? 15. What is the solution set of 2sin^2(x)-3sin(x)-2=0 where 0<=x<=2pi Click here to see answer by Fombitz(13828)

 Question 375796: Height of tsunami waves: when waves generated by tsunamis approach shore, the height of the waves gennerally increases. Understanding the factors that contribute to this increase can aid in controlling potential damage to areas at risk. Greens law tells us how water depth affects the height of a tsunami wave. If a tsunami wave has height H at an ocean depth D, and the wave travels to a location of water depth d, then the new height h of the wave is given by h= HR^0.25, where R is the water depth ratio given by R=D/d. A.) Calculate the height of a tsunami wave in water 25 feet deep if its height is a 3 feetat its point of orgin in water 15,000 feet deep. B.) If water depth decreases by half, the depth ratio R is doubled. How is the height of the tsunami wave affected? Helpful hints: a power function has a form of: f(x)= cx^k Please help;) Click here to see answer by ankor@dixie-net.com(15622)

 Question 375830: Stopping an Oil Tanker: It has been shown that if an oil tanker stops its engines, then its velocity will decrease exponentially. Suppose that captin shuts off the engines when the speed of the tanker is 20 mph and one minute later the speed of the tanker is 18 mph. What is the speed of the tanker after one hour? Click here to see answer by ankor@dixie-net.com(15622)

 Question 376424: define 2^3^2 to be 2^(3^2). is 2^3^2 the same with 2^(3^2)? Click here to see answer by Alan3354(30924)

 Question 376785: Verify that 2i is a zero of P(x)= x^4-2x^3-11x^2-8x-60 Also find the remaining zeros. Click here to see answer by jsmallt9(3296)

 Question 376787: Factor to find all the real zeros of P(x)= 2x^3+5x^2-12x Click here to see answer by jsmallt9(3296)

 Question 377449: The question says that one square metre measures 1m by 1m It then asks for you to write 1m^2 in square millinetres as a product of powers and as a single power. For the product of powers part, I wrote down 1^1 x 1^1= 1^2. Click here to see answer by mananth(12269)

 Question 377267: State the degree and leading coefficient of each polynomial in one variable. if it is not a polynomial in one variable, explain why. Q1: (3x^2+1)(2x^2-9) Q2: 1/5a^3-3/5a^2+4/5a Click here to see answer by robertb(4012)

 Question 377497: How do I simplify this and find x? log4(x-4) + log4(x+2) = log7(49) Click here to see answer by vasumathi(46)