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5-3x-3-5-3x-5-615-solve-for-x-




Question Number 57368 by problem solverd last updated on 03/Apr/19
5^(3x−3) −5^(3x) −5=615  solve for x
$$\mathrm{5}^{\mathrm{3}{x}−\mathrm{3}} −\mathrm{5}^{\mathrm{3}{x}} −\mathrm{5}=\mathrm{615} \\ $$$$\mathrm{solve}\:\mathrm{for}\:{x} \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 03/Apr/19
5^(3x) =a  (5^(3x) /5^3 )−5^(3x) −5=615  (a/(125))−a=620  ((a−125a)/(125))=620  −124a=620×125  a=((−620×125)/(124))=((−5×125)/1)=−5^4   5^(3x) =−5^4   here is the problem arises..  5^(3x)  can not be negetive...
$$\mathrm{5}^{\mathrm{3}{x}} ={a} \\ $$$$\frac{\mathrm{5}^{\mathrm{3}{x}} }{\mathrm{5}^{\mathrm{3}} }−\mathrm{5}^{\mathrm{3}{x}} −\mathrm{5}=\mathrm{615} \\ $$$$\frac{{a}}{\mathrm{125}}−{a}=\mathrm{620} \\ $$$$\frac{{a}−\mathrm{125}{a}}{\mathrm{125}}=\mathrm{620} \\ $$$$−\mathrm{124}{a}=\mathrm{620}×\mathrm{125} \\ $$$${a}=\frac{−\mathrm{620}×\mathrm{125}}{\mathrm{124}}=\frac{−\mathrm{5}×\mathrm{125}}{\mathrm{1}}=−\mathrm{5}^{\mathrm{4}} \\ $$$$\mathrm{5}^{\mathrm{3}{x}} =−\mathrm{5}^{\mathrm{4}} \\ $$$${here}\:{is}\:{the}\:{problem}\:{arises}.. \\ $$$$\mathrm{5}^{\mathrm{3}{x}} \:{can}\:{not}\:{be}\:{negetive}… \\ $$$$ \\ $$
Commented by MJS last updated on 04/Apr/19
for x∈C we′d get  x=(4/3)+((2n+1)/(3ln 5))πi with n∈Z
$$\mathrm{for}\:{x}\in\mathbb{C}\:\mathrm{we}'\mathrm{d}\:\mathrm{get} \\ $$$${x}=\frac{\mathrm{4}}{\mathrm{3}}+\frac{\mathrm{2}{n}+\mathrm{1}}{\mathrm{3ln}\:\mathrm{5}}\pi\mathrm{i}\:\mathrm{with}\:{n}\in\mathbb{Z} \\ $$

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