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Solve for x (without using a calculator):
log base 3 of x^2= 2log base 3 of 4-4log base 3 of 5

Solve each of the inequalities:
(a) x^2+2x-3<(or equal to)0
(b) (2x-1)/(3x-2)<(or equal to)1

Any help is appreciated!

  • math (1 of 3) -

    log base(3)x^2 = 2log(3)4 - 4log(3)5
    = log(3)[4^2/5^4]
    Therefore x^2 = 16/625
    x = 4/25 = 0.16

  • math (2 of 3) -

    <<(a) x^2+2x-3<(or equal to)0 >>

    First solve
    x^2 +2x -3 =0
    (x+3)(x-1) = 0
    x = -3 or 1
    Between those points, for example at x=0, the function is negative.
    (f(0)= -3, for example.)
    -3 <_ x <_ 1 is the answer

  • math (#3 of 3) -

    <<(2x-1)/(3x-2)<(or equal to)1>>
    When equal to 1,
    2x-1 = 3x-2
    x = 1
    If you go on the positive side if 1, for example at x = 2,
    (2x-1)/(3x-2) = 3/5 which is <1

    Any x >_ 1 satisfies the inequality

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