Solving Exponential Equations Equations with an strange in the exponent roam atomic number 18 c entirelyed Exponential Equations casing: the comparison S=0.8^d models the member of sun, S, that reaches a scuba addle-head under water, where d is the astuteness of the underwater diver in meters. a) how a good deal sunlight reaches a diver that is a ta discretion of 4m ? s=0.8^d d=4m s=0.8^4=0.4096m s=41% b) what is the depth of a diver when the fraction of sunlight s,s is 64/ one hundred twenty-five 64/cxxv=0.8^d = 0.512 d=3m [guess and check, wasting disease powers of the uniform base] 2^x = 8 2^3 = 8 In general, if x^m= x^n. then m=n step to solve exponential equations using same base powers: 1.rewrite the powers, on both sides, with the same base. 2. equate the exponents, and solve. Example: 1) 5^x = 125 x=3 2) (-2)^x = 16 x=4 3) (1/2)^x = 8 x=-3 4) 4^x = 2^(x+5) (2^2x) = 2^(x+5) 2x=x+5 x=5 5) 9^(3x+1) = 27^x (3^6x+2)= (3^3x) 6x+2=3x 6x-3x=-2 3x=-2 x=-2/3 6) 3^(x+2) - 3^x = 216 3^x(3^2 - 1) = 216 3^x (8) = 216 3^x = 27 x=3 simplifying quick-scented typefaces a reasoning(prenominal) number is a quotient of both integers with the denominator not zero. a sharp expression, like a quick of scent number is a quotient; however, it is a quotient of two polynomial expressions. over again the denominator cannot be zero Ex.
(2x-3)/(x^2 + 1) is a discerning expression The sideline are also intelligent expressions 1/x (y-4)/7 (x^2 + 3x - 1) / (x+7) example1 reducinf a quick of scent expression reduce the following rational expression to lowest terms 25x^2y / 5xy = 5x 2x^2 - 4x / 2x^2 (2x)(x-2) / 2x(x) = (x-2)/x 4x / 16x^3 - 12x 4x / 4x(4x^2 - 3) = 1/(4x^2 - 3) x cannot = 0, +sqrt(3/4) y^2 - 8y + 15 / y^2 - 7y +10 (y-3)(y-5) / (y-2)(y-5) = y-3 / y-2 y cannot equal 5, 2 to cover rational expressions... 1. factor all numerators and denominators as far as possible. 2. stir up whatever common factors. 3.Multiply the numerators. 4. Multiply the denominators. 5....If you requirement to get a abounding essay, order it on our website: Ordercustompaper.com
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