Solving exponential equations using exponent rules

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  1. Solve for "xx", with common base
    1. 2x=252^x=2^5
    2. 32x+1=311 3^{2x+1}=3^{11}
  2. Solve for "xx ", by converting to common base
    1. 34x−8=27−2x3^{4x-8}=27^{-2x}
    2. 87−2x=165x+10 8^{7-2x}=16^{5x+10}
    3. 3x4−45=815729 3^{\frac{x}{4}-\frac{4}{5}}=81{^5}\sqrt{729}
    4. 1812−x=274x+5\frac{1}{81^{2-x}}=27^{4x+5}
    5. (14)1−2x=8x−3(\frac{1}{4})^{1-2x}=8^{x-3}
    6. 9x+2=(34x−3)(35)9^{x+2}=(3^{4x-3})(3^5)
    7. (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
    Topic Notes