Pre-Calculus

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Could someone check my answers?

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

Answer- x= 8/5

26. 9^(2x+1)=81

Answer- x= 1/2

27. 1/4=2^3x

Answer- x= -2/3

28. 1/27=3^2x

Answer- x= -3/2

29. 9^x=27

Answer- x= 3/2

30. 32^x=4

Answer- x= 2/5

31. 27^(x+1)=9

Answer- x= 1/2

32. 125^(x-2)=25

Answer- x= 7/2

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

Answer- x= -2

34. 4^(3x-7)=32^2x

I'm having problems with number 34.

  • Pre-Calculus -

    34.
    4^(3x-7) = 32^x
    (2^2)^(3x-7) = (2^5)^x
    2^(6x-14) = 2^(5x)

    6x - 14 = 5x
    x = 14

    #31 and #32 are also incorrect, the rest are good

    31.

    27^(x+1) = 9
    (3^3)^(x+1) = 3^2
    3^(3x+3) = 3^2
    3x+3=2
    x = -1/3

    32.

    125^(x-2)x = 25
    (5^3)^(x-2) = 5^2
    5^(3x-6) = 5^2
    3x-6=2
    3x = 8
    x = 8/3

  • Pre-Calculus -

    Thank you

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