Math

Solving Exponential Equations Equations with an unknown in the exponent site atomic material body 18 called Exponential Equations Example: the impactity S=0.8^d models the fraction of sunshine, S, that reaches a scuba plunger under water, where d is the deepness of the diver in meters. a) how practically sunlight reaches a diver that is a ta wisdom 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 64/125 64/125=0.8^d = 0.512 d=3m [guess and check, use powers of the said(prenominal) base] 2^x = 8 2^3 = 8 In general, if x^m= x^n. then m=n step to solving 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 rational observation, analogous a rational number is a quotient; however, it is a quotient of devil polynomial expressions. over again the denominator cannot be zero Ex.

(2x-3)/(x^2 + 1) is a rational expression The following are withal rational expressions 1/x (y-4)/7 (x^2 + 3x - 1) / (x+7) example1 reducinf a rational expression reduce the following rational expr ession 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 multiply rational expressions... 1. factor all numerators and denominators as far as possible. 2. stir up any commonplace factors. 3.Multiply the numerators. 4. Multiply the denominators. 5....If you want to get a full essay, point it on our website: BestEssayCheap.com

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