Math

Solving Exponential Equations Equations with an unknown in the exponent point atomic phone number 18 called Exponential Equations Example: the comparability S=0.8^d models the fraction of temperateness, S, that reaches a scuba addle-head under water, where d is the deepness of the diver in meters. a) how such(prenominal) sunlight reaches a diver that is a ta enlightenment 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 resembling 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 demeanor, the likes of a rational number is a quotient; however, it is a quotient of deuce polynomial expressions. over again the denominator cannot be zero Ex.

(2x-3)/(x^2 + 1) is a rational expression The following are alike rational expressions 1/x (y-4)/7 (x^2 + 3x - 1) / (x+7) example1 reducinf a rational express ion reduce the following rational expressio! n 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 pit 5, 2 to multiply rational expressions... 1. factor all numerators and denominators as far as possible. 2. stir up any parking lot factors. 3.Multiply the numerators. 4. Multiply the denominators. 5....If you want to get a full essay, tack together it on our website: BestEssayCheap.com

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