Math

Solving Exponential Equations Equations with an unknown in the exponent put atomic image 18 called Exponential Equations Example: the par S=0.8^d models the fraction of cheer, S, that reaches a scuba piston under water, where d is the deepness of the diver in meters. a) how overmuch sunlight reaches a diver that is a ta discernment 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 homogeneous base] 2^x = 8 2^3 = 8 In general, if x^m= x^n. then m=n step to solving exponential function 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 conceptualisation, uniform a rational number is a quotient; however, it is a quotient of both polynomial expressions. over again the denominator cannot be zero Ex.

(2x-3)/(x^2 + 1) is a rational expression The following are in addition rational expressions 1/x (y-4)/7 (x^2 + 3x - 1) / (x+7) example1 reducinf a rational expression reduce the follo wing rational expression to lowest terms 25! x^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 commensurate 5, 2 to multiply rational expressions... 1. factor all numerators and denominators as far as possible. 2. stir up any usual factors. 3.Multiply the numerators. 4. Multiply the denominators. 5....If you want to get a full essay, tramp it on our website: BestEssayCheap.com

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