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# Recent problems solved by 'funmath'

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 logarithm/61801: This question is from textbook Please help with the following problem: e^x = 2^x+11 solutions Answer 42616 by funmath(2925)   on 2006-11-17 13:34:57 (Show Source): You can put this solution on YOUR website!e^x = 2^(x+1) ln(e^x)=ln(2^(x+1)) xln(e)=(x+1)ln(2) x(1)=(x+1)ln(2) x=xln(2)+ln(2) x-xln(2)=ln(2) x(1-ln(2))=ln(2) x(1-ln(2))/(1-ln(2))=ln(2)/(1-ln(2)) x=ln(2)/(1-ln(2)) x=2.258891353 approximatlely. Happy Calculating!!!
 Equations/61883: what is the value of e in 7e+4=5e-81 solutions Answer 42615 by funmath(2925)   on 2006-11-17 13:21:09 (Show Source): You can put this solution on YOUR website!7e+4=5e-8 7e-5e+4=5e-5e-8 2e+4=-8 2e+4-4=-8-4 2e=-12 2e/2=-12/2 : Check: 7(-6)+4=5(-6)-8 -42+4=-30-8 -38=-38 We're right!!! Happy Calculating!!!!
 Functions/61882: Use the defination of inverse function to show analytically that f and g are inverse: f(x) = 4x+3 and g(x)= x-3/41 solutions Answer 42614 by funmath(2925)   on 2006-11-17 13:17:29 (Show Source): You can put this solution on YOUR website!Use the defination of inverse function to show analytically that f and g are inverse: In order to be inverses, their composites have to equal x. f(x) = 4x+3 and g(x)= (x-3)/4 (fog)(x)=f(g(x))=f((x-3)/4)=4((x-3)/4)+3=x-3+3=x (gof)(x)=g(f(x))=g(4x+3)=((4x+3)-3)/4=4x/4=x They are inverses of each other. Happy Calculating!!!!
 Exponential-and-logarithmic-functions/61854: I am having trouble solving these problems could someone help me? 7^2x+3=49^8-x1 solutions Answer 42613 by funmath(2925)   on 2006-11-17 13:08:51 (Show Source): You can put this solution on YOUR website! 2x+3=2(8-x) 2x+3=16-2x 2x+2x+3=16-2x+2x 4x+3=16 4x+3-3=16-3 4x=13 4x/4=13/4 Happy Calculating!!!!
 Functions/61877: is the number 47 a composite number?1 solutions Answer 42612 by funmath(2925)   on 2006-11-17 12:37:30 (Show Source): You can put this solution on YOUR website!47 is prime, it's only factors are one and itself. No, it is not composite. Happy Calculating!!!
 Distributive-associative-commutative-properties/61876: wich number is a prime number 1 12 31 991 solutions Answer 42610 by funmath(2925)   on 2006-11-17 12:26:38 (Show Source): You can put this solution on YOUR website!wich number is a prime number 1 12 99 : 1 is unusual because it seams like it should be prime, but the math gods decided it wasn't/ 12=2*6, 3*4 so it's a composite number. 99=9*11,3*33 so it's a composite number as well The only factors of 31 is 1*31 so it's prime. Happy Calculating!!!
 Functions/61863: I need some help with a word problem Please. A bank compounds interest continuously. If you invest \$500 at 4% at that bank for 5 years, what will your balance be? Use formula A= 500e^0.04t where A is the balance in the account and t is in years.1 solutions Answer 42608 by funmath(2925)   on 2006-11-17 11:57:54 (Show Source): You can put this solution on YOUR website!A bank compounds interest continuously. If you invest \$500 at 4% at that bank for 5 years, what will your balance be? Use formula A= 500e^0.04t where A is the balance in the account and t is in years. A=\$610.70 Happy Calculating!!!
 Exponential-and-logarithmic-functions/61872: Solve the equation 2^3x=4^x-1 by getting a common base.1 solutions Answer 42607 by funmath(2925)   on 2006-11-17 11:41:36 (Show Source): You can put this solution on YOUR website!Solve the equation 2^3x=4^(x-1) by getting a common base. 3x=2(x-1) 3x=2x-2 3x-2x=2x-2x-2 Check: We're right!!!! Happy Calculating!!!
 logarithm/61874: Rewrite in a single quanity ln(5) + 2ln(x)-3ln(z)1 solutions Answer 42603 by funmath(2925)   on 2006-11-17 11:26:32 (Show Source): You can put this solution on YOUR website! Happy Calculating!!!
 Equations/61870: what is the value of p in 6p-7=2p+9 and how did you get that answer?1 solutions Answer 42602 by funmath(2925)   on 2006-11-17 11:20:01 (Show Source): You can put this solution on YOUR website!Do the inverse operations to both sides in order to isolate p. (If something that you need to move is added, subtract it, if its subtracted, add it, if it's multiplied, divide it, if it's divided multiply it.) 6p-7=2p+9 6p-2p-7=2p-2p+9 4p-7=0+9 4p-7=9 4p-7+7=9+7 4p=16 4p/4=16/4 : Check by subtituting 4 in for p in the original equation and see if both sides =. 6(4)-7=2(4)+9 24-7=8+9 17=17 We're right!!!! Happy Calculating!!!
 Exponential-and-logarithmic-functions/61855: Could someone please help me solve: 4^(2-6x)=8121 solutions Answer 42601 by funmath(2925)   on 2006-11-17 11:12:55 (Show Source): You can put this solution on YOUR website!4^(2-6x)=812 ln(4^(2-6x))=ln(812) (2-6x)ln(4)=ln(812) (2-6x)ln(4)/ln(4)=(ln(812))/(ln(4)) 2-6x=(ln(812)/(ln(4)) -2+2-6x=(ln(812))/(ln(4))-2 -6x=4.832667959-2 -6x=2.832667959 -6x/-6=2.832667959/-6 x=-.4721113264 Happy Calculating!!!!
 logarithm/61858: Could someone help show me how to expand: log2(x^4y^3/5n^2) Thank you.1 solutions Answer 42599 by funmath(2925)   on 2006-11-17 10:52:30 (Show Source): You can put this solution on YOUR website! Happy Calculating!!!
 logarithm/61861: How do I work this? log(logb)=0.71 solutions Answer 42598 by funmath(2925)   on 2006-11-17 10:41:21 (Show Source): You can put this solution on YOUR website!log(logb)=0.7 logb=10^0.7 b=10^(10^0.7) b=102771.415 : Happy Calculating!!!
 Exponential-and-logarithmic-functions/61856: Please find dy/dx using implicit differentiation: y^2+e^y=ln x^2+4 Thanks!1 solutions Answer 42596 by funmath(2925)   on 2006-11-17 10:22:52 (Show Source): You can put this solution on YOUR website!y^2+e^y=ln x^2+4 2yy'+e^yy'=2/x+0 y'(2y+e^y)=2/x y' y'= Happy Calculating!!!
 logarithm/61860: Is the expression log1 512 an expression that can be evaluated?1 solutions Answer 42592 by funmath(2925)   on 2006-11-17 10:15:52 (Show Source): You can put this solution on YOUR website!Is the expression log1 512 an expression that can be evaluated? No. There is no power you can raise 1 to to get 512. : Another thing you can do to prove this to yourself is to try to solve it using change of bases. log1 512=(ln(512))/(ln(1))=ln(512)/0=undefined : You can try putting ln(512)/ln(1) into your calculator, the ti-83 says, "ERR:DIVIDE BY 0". : Happy Calculating!!!!
 logarithm/61859: Could someone help show how to express this in a single log and simplify if possible? log10 x + log10 y1 solutions Answer 42588 by funmath(2925)   on 2006-11-17 10:10:45 (Show Source): You can put this solution on YOUR website!log10 x + log10 y When logs of like bases are added you can write them this way. log10 (xy) It is similar to rules involving exponents Happy Calculating!!!!
 Equations/61864: can you help solve this equation? 3x^2+9bx=ax +3ab So far I've tried 3x^2+9bx-ax-3ab=0 -(a-3x)(3b+x)=0 I am to solve for x Thanks1 solutions Answer 42587 by funmath(2925)   on 2006-11-17 10:06:46 (Show Source): You can put this solution on YOUR website!When I factored I got (I don't know where you got the -, but you would get the same thing I got if you solved for x.) If the directions say solve, you solve for x. (3x-a)*(x+3b)=0 3x-a=0 and x+3b=0 3x-a+a=0+a and x+3b-3b=0-3b 3x=a and x=-3b 3x/3=a/3 and x=-3b x=a/3 and x=-3b : Check when x=a/3 (3(a/3)-a)(a/3+3b)=0 (a-a)(a/3+3b)=0 0(a/3+3b)=0 0=0 When x=-3b (3(-3b)-a)(-3b+3b)=0 (-9b-a)(0)=0 0=0 We're right!!! Happy Calculating!!!
 Rational-functions/61752: use synthetic division: Problem: x(to the third) -2x(squared) -x +2 divided by x-2 the answer I got was: x(squared) + x +4/x-2 but i'm not sure if I did it right, please help!1 solutions Answer 42497 by funmath(2925)   on 2006-11-16 13:54:06 (Show Source): You can put this solution on YOUR website!x^3-2x^2-x +2 divided by x-2 2|1 -2 -1 2 .|___2__0_-2_ ''1 0 -1 0 Therefore, the solution is x^2+0x-1= : Happy Calculating!!!
 Linear-systems/61694: This question is from textbook Alegbra Concepts and applications please help Use substitution to solve for x and y 3x - y = 3 y = 2x - 11 solutions Answer 42493 by funmath(2925)   on 2006-11-16 13:13:26 (Show Source): You can put this solution on YOUR website!Use substitution to solve for x and y E1: 3x - y = 3 E2: y = 2x - 1 : Substitute 2x-1 from E2 in for y in E1 and solve for x. : 3x-(2x-1)=3 3x-2x+1=3 x+1=3 x+1-1=3-1 x=2 : Substitute 2 in for x in E2 and solve for y. : y=2(2)-1 y=4-1 y=3 : Therefore the solution is (x,y)=(2,3) : Sanity Check, does that solution work for both E1 and E2. 3(2)-(3)=3--->6-3=3--->3=3 E1 Checks 3=2(2)-1--->3=4-1--->3=3 E2 Checks Happy Calculating!!!
 Linear-systems/61681: I sent this problem in and made an error on how it has to be solved The system is to be solved by addition. 5x-3y=13 4x-3y=11 Thanks 1 solutions Answer 42451 by funmath(2925)   on 2006-11-16 08:27:03 (Show Source): You can put this solution on YOUR website!E1: 5x-3y=13 E2: 4x-3y=11 : This is the elimination method (also known as the addition method). Multiply the E2 by -1 and add it to E1 and the y's will be eliminated so that you can solve for x. : -1(4x-3y)=-1(11) --> -4x+3y=-11 : 5x-3y=13 -4x+3y=-11 __________ x+0=2 x=2 : Substitute 2 in for x in either equation and solve for y. 4(2)-3y=11 8-3y=11 8-8-3y=11-8 -3y=3 -3y/-3=3/-3 y=-1 : Therefore, your solution is: (x,y)=(2,-1) Happy Calculating!!!