Math, Precalc

posted by Susan

(3^x)+(5^{x+3})=(3^{x+4})-(1/3)*( 5^{x+2}).

Solve

  1. Anonymous

    3^x + 5^(x+3) - 3^(x+4) + (1/3)5^(x+2)= 0
    3^x(1 - 3^4) + 5^(x+2)(5 + (1/3)(1) ) = 0
    -80(3^x) + (16/3)(5^(x+2) = 0
    times -3/16
    15(3^x) - 5^(x+2) = 0
    15(3^x) = 5^(x+2)
    divide by 5
    3(3^x) = 5^(x+1)
    3^(x+1) = 5^(x+1)
    this can only be true if x = -1
    that is, if 3^0 = 5^0 , which is true

  2. Reiny

    3^x + 5^(x+3) - 3^(x+4) + (1/3)5^(x+2)= 0
    3^x(1 - 3^4) + 5^(x+2)(5 + (1/3)(1) ) = 0
    -80(3^x) + (16/3)(5^(x+2) = 0
    times -3/16
    15(3^x) - 5^(x+2) = 0
    15(3^x) = 5^(x+2)
    divide by 5
    3(3^x) = 5^(x+1)
    3^(x+1) = 5^(x+1)
    this can only be true if x = -1
    that is, if 3^0 = 5^0 , which is true

  3. Steve

    just start by combining like powers:

    (3^x)+(5^{x+3})=(3^{x+4})-(1/3)*( 5^{x+2})
    3^x + 125*5^x = 81*3^x - 3^-1 * 25*5^x

    3*3^x + 375*5^x = 243*3^x - 25*5^x
    (375+25)*5^x = (243-3)*3^x
    400*5^x = 240*3^x
    5*5^x = 3*3^x
    5^(x+1) = 3^(x+1)
    (x+1)log5 = (x+1)log3
    (x+1)(log5-log3) = 0
    x = -1

Respond to this Question

First Name

Your Answer

Similar Questions

  1. Math

    Precalc stuff.. square root of z-1= square root of z +6 are you solving for z?
  2. PreCalc

    Solve for the variable m^2 + 2m +3 > = 0
  3. precalc

    1. Solve |2x + 5|< 9
  4. Math- Precalc

    could someone please help me solve this problem... e^x - 12e^(-x) - 1
  5. precalc

    solve x/x^2-4 - 1/x+2=2
  6. Math - PreCalc (12th Grade)

    Use the inverse matrix to solve this system of equations: 4x+3y=7.5 7x+9z=14 4y-z=8.3 4,3,0 7,0,9 0,4,-1
  7. PreCalc

    Solve each inequality: (1/(2b+1)) + (1/(b+1)) > (8/15) (2/(x+1)) < 1 - (1/(x-1)) My teacher told me the answer is in interval notation, and that a number line is used to solve.
  8. precalc

    i also need help with these two questions: 1/r=1/r1 +1/r2 solve for r1 and: f= G(mM/r^2); solve for m
  9. precalc

    (-2)^x = - 1/128 solve for x
  10. PreCalc

    Solve: (x-1)/(x)+(x-2)/(x)+(x-3)/(x)+...+(1)/(x)=3; X belongs to N

More Similar Questions