Solving exponential equations using exponent rules

Solving exponential equations using exponent rules

Lessons

  • 1.
    Solve for "xx", with common base
    a)
    2x=252^x=2^5

    b)
    32x+1=311 3^{2x+1}=3^{11}


  • 2.
    Solve for "xx ", by converting to common base
    a)
    34x8=272x3^{4x-8}=27^{-2x}

    b)
    872x=165x+10 8^{7-2x}=16^{5x+10}

    c)
    3x445=815729 3^{\frac{x}{4}-\frac{4}{5}}=81{^5}\sqrt{729}

    d)
    1812x=274x+5\frac{1}{81^{2-x}}=27^{4x+5}

    e)
    82x4=(116)5x8^{2x-4}=(\frac{1}{16})^{5-x}

    f)
    (14)12x=8x3(\frac{1}{4})^{1-2x}=8^{x-3}

    g)
    9x+2=(34x3)(35)9^{x+2}=(3^{4x-3})(3^5)

    h)
    (3431000)12x=(107)x(\frac{343}{1000})^{-\frac{12}{x}}=(\frac{10}{7})^x


  • 3.
    Solve: 5(9x)+40(3x)45=05(9^x)+40(3^x)-45=0