Pre-Calculus

posted by .

I'm having problems understanding how to do these problems.

25. 32^(2x-3)=2

27. 1/4= 2^3x

29. 9^x=27

33. 81^(x-1)= 27^2x

  • Pre-Calculus -

    recall that log(x^a) = a * log x

    25)
    32^(2x-3) = 2
    take log of both sides to get
    (2x-3) log 32 = log 2
    2x-3 = log 2 / log 32
    Now recall that loga/logb = log_b(a)
    so, log2/log32 = log_32(2) = 1/5
    since 2^5 = 32, 2 = 32^(1/5), so log_32(2) = 1/5

    2x-3 = 1/5
    2x = 16/5
    x = 8/5

    Or, we could have started out by noting that 2 = 32^(1/5), so equating powers of 32,
    2x-3 = 1/5
    ...

    27)
    similarly, since 1/4 = 2^-2,
    -2 = 3x
    x = -2/3

    29)
    Since 3= 9^1/2, 27 = 3^3 = 9^3/2, so
    x = 3/2

    33)
    27 = 3^3
    81 = 3^4, so
    27 = 81^(3/4)
    equating powers,
    x-1 = 2x(3/4)
    x-1 = 3x/2
    x/2 = -1
    x = -2
    check:
    81^-3 = 3^-12
    27^-6 = 3^-12

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Pre-Calculus

    I am having trouble with several problems: 1) Find the coordinates of the center, foci, and the vertices, and the equations of the asymptotes of the graph of the equation (x+1)^2/2 - y^2/8 =1 2) Write the standard form of the equation …
  2. Pre-Calculus

    I am having trouble with several problems: 1) Find the coordinates of the center, foci, and the vertices, and the equations of the asymptotes of the graph of the equation (x+1)^2/2 - y^2/8 =1 2) Write the standard form of the equation …
  3. Pre-Calculus

    I am in Honors Pre-Calculus and am having a hard time understanding my teacher. I feel so stupid. Does anyone have any suggestions on a website that might give me some insight into what I am doing wrong?
  4. Math

    I am having problems understanding how to solve problems like the following: a2 + b2 = c2 Please help me where I can understand solving problems such as the one above.
  5. Pre Algebra

    I am having problems with inequality problems. The opposite of g is at least -5. Write an inequality and solve.
  6. Pre-algebra

    I have some practice problems, and I need to have them worked out, showing your work. I will gain a better understanding of these problems by practicing them. Thank you. (6x+1)(x^2-9x+5) (2x^4+3)(4x^3+2) (12y^3+8y^2+20y)divided 2y …
  7. Pre-algebra

    I have some practice problems, and I need to have them worked out, showing your work. I will gain a better understanding of these problems by practicing them. Thank you. (6x+1)(x^2-9x+5) (2x^4+3)(4x^3+2) (12y^3+8y^2+20y)divided 2y …
  8. pre calculus

    Hi, I am having a problem trying to find and understanding how to find the extreme values. I have a problem which I can't do. Will someone please explain for me how to do it. I would like to be able to do other similar problems. This …
  9. pre calculus

    Hi, I am having a problem trying to find and understanding how to find the extreme values. I have a problem which I can't do. Will someone please explain for me how to do it. I would like to be able to do other similar problems. This …
  10. algebra homework help

    student missed 11 problems on a Chemistry test and received a grade of 65%. If all the problems were of equal value, how many problems were on the test?

More Similar Questions