solve-for-x-R-x-x-n-a-with-n-a-R-find-also-the-range-of-a-such-that-a-solution-exists- Tinku Tara June 3, 2023 Algebra 0 Comments FacebookTweetPin Question Number 139805 by mr W last updated on 01/May/21 solveforx∈R\boldsymbolx\boldsymbolx\boldsymboln=\boldsymbolawithn,a∈R+findalsotherangeof\boldsymbolasuchthatasolutionexists. Commented by mr W last updated on 01/May/21 ithoughtaboutthisgeneralequationforalongtimeandtriedtofindaformulatoexpressthesolution.weknowifn=a,thesolutionforxxa=aisthesameasforxa=a,i.e.x=aa.butwhatisthesolutionforthegeneralcasewithn≠a? Answered by mr W last updated on 02/May/21 herethesolutionigotforthegeneralcasexxn=a.xxn=ax=a1xn=elnaxnxn=enlnaxn1xnenlnaxn=1nlnaxnenlnaxn=nlnanlnaxn=W(nlna)xn=nlnaW(nlna)⇒x=nlnaW(nlna)nsuchthatarealrootexists,W(nlna)mustbedefined.thisisthecaseifnlna⩾−1e,i.e.a⩾e−1ne=1ene.therefore:fora<1ene⇒norootfora=1ene⇒onerootfor1ene<a<1⇒tworootsfora⩾1⇒onerootexample:xx5=10⇒x=5ln10W(5ln10)5≈5ln101.8359285=1.443664example:xx3=910⇒x=3ln0.9W(3ln0.9)3≈{3ln0.9−1.6564043=0.5757193ln0.9−0.5452573=0.833808 Commented by Tawa11 last updated on 23/Jul/21 greatgreat Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Evaluate-the-integral-a-b-a-b-a-a-b-a-2-a-a-b-b-a-2-dt-In-which-a-b-are-the-derivatives-of-a-b-with-respect-to-t-Next Next post: Question-74274 Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.