[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-69229-es":3,"doc-seo-69229-110":31,"detail-sidebar-cat-0-es-110":84},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},69229,2336475104957,"Seraphina","https://ap-avatar.wpscdn.com/avatar/22000c4c6bd8a5076e1?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786593998035447633",38,"Examen","Ecuaciones Exponenciales","Guía de ejercicios de matemáticas sobre ecuaciones exponenciales, centrada en hallar valores de x, simplificar expresiones con potencias y exponentes, y resolver ecuaciones y sistemas lineales vinculados mediante potencias. Incluye apartados con ejercicios aplicados a ecuaciones de la forma a^{f(x)}=b^{g(x)}, además de tareas de simplificación algebraica y resolución por cambio de variable. Se aportan soluciones finales para comprobación y práctica progresiva de métodos y propiedades de potencias.","Departamento de Matemáticas I. E.S. Arroyo de la Miel  \n.  \nECUACIONES EXPONENCIALES.  \n1. Halla \"x\":  \na) 2x+1 = 4x b) 2x=1/16 c) 3x+1 = 9x-2  \nd) 25x =  5  \nh) 2x2-3 = ~~ ~~14  \ne) 25x = ~~ ~~15 i) 3x-1 = 3 3  \nf) 3x2-2 = 9  \nj) 2x+1 = 16 x  \ng) 32x-3 = 81  \nk) 32x-1 = 81x  \nSol: a) x= 1; b) x=-4; c) x=5; d) x= 1/4; e) x=-1/2; f) x2; g) 7/2; h) x1; i) 4/3; j) 1/3; k) -1/2  \n2. Halla \"x\":  \na) 271/3 = x  \ne) 4x= 32  \ni) 􀂧􀂨  1  􀂷􀂸x = 100  \n􀂩 10 􀂹 m) 103x = 100  \nb) x1/2 = 5  \nf) x3/2 = 8  \nj) 3x= 9x+1  \nn) 102x-1 = 0,01  \nc) 32x= 2  \ng) 32x = 27  \nk) 92x = 27  \nd) x3/2 = 27  \nh) 10x= 0,001  \nl) 22x = 82  \nSol: a) x=3; b) x=25; c) x=1/5; d) x=9; e) x=5/2; f) x=4; g) 3/2; h) x=-3; i) -2; j) -2; k) x=3/4; l) x=3;  \nm) x=2/3; n) x=-1/2  \n3. Simplifica las siguientes expresiones:  \na) 3x+2 . 9x-1 . 32 b) 2x-1 . 2x2-1 . 23-xd) 3x+21~~ ~~.~~ ~~x3x~~ ~~ e) 2x+1~~ ~~x3-2~~ ~~.~~ ~~2x-1 g) 21~~ ~~.+232-xx-1~~ ~~ h) 33xx+1~~ ~~3.~~ ~~xx1  \nSol: a) 33x+2 ; b) 2x2+1 ; c) 2-x-1 ; d) 2 . 3-x ; e) 7 g) ( e3 - 1 ) e-x-1  \n. 23-x ; f) 􀂧􀂨 􀂩  \nc) 4x8x--21  \nx-1 + x+3 f) e~~ ~~4x~~ ~~e~~ ~~  \ne  \nx+1 x-2  \ni) e~~ ~~2~~ ~~-1e~~ ~~e  \n1 3 􀂷  \n~~ ~~ + e 􀂸  \ne 􀂹  \n-3x 24 2 e ; g)  3  ; h) 32x-x ;  \n4. Resuelve:  \na) 3-x + 9x+1 = 4 b) 32x+3 = 2187 c) 3xx+-12 = ~~ ~~19  \nd) 3x2-3x+3 = 3 e) 10 ~~ ~~xx-11 = 10 f) 32x-1 - 3x+1 = 0  \ng) 52x+1 + 3 . 56x-3 = 500 h) 4x-2 - 2x+1 = -12 i) 32 (x+2) - 4 . 3x - 77 = 0 Sol: a) x=-1; b) x=2; c) x= 1; d) x=1, x=2; e) x=2; f) x=2; g) 1; h) x=3; i) x=0  \nDepartamento de Matemáticas  \n5. Resuelve los siguientes sistemas:  \n􀂭  \na) 􀂮  \n􀂯  \n􀂭  \nd) 􀂮  \n􀂯  \n􀂭  \ng) 􀂮  \n􀂯  \n􀂭  \ni) 􀂮  \n􀂯  \n3x+ y = 81 3y-x= 9  \n2x + 3y = 7 22x+1 - 32y = 23  \n􀂭  \nb) 􀂮  \n􀂯  \n􀂭  \ne) 􀂮  \n􀂯  \n2 . 3x+1 - 3y-1 = 15 5 . 3x+2 - 3y+1 = 108 2 . 5x - 2 . 3y+2 = 32  \n5x + 3y+1 = 28  \n3x + 3y = 36  \n3y-x= 3 22x-y = 32 3x-2y = 3  \n􀂭  \nc) 􀂮  \n􀂯  \n􀂭  \nf) 􀂮  \n􀂯  \n􀂭  \nh) 􀂮  \n􀂯  \n􀂭  \nj) 􀂮  \n􀂯  \nI. E.S. Arroyo de la Miel  \n2x + 2y = 20  \n2y+x= 64  \n3x . 9y = 38 2x-1 . 2y+1 = 26  \n3 . 2x - 2 . 3y = -42  \n5 . 2x+1 - 4 . 3y-1 = 4 3x - 2y+1 = 235 3x-1 - 2y-1 = 79  \nSol: a) x=1, y=3; b) x=2, y=3; c) x=4, y=2; x=2, y=4; d) x=2, y=1; e) x=3, y=1; f) x=4, y=2; g) x=1, y=2;  \nh) x=2, y=3; i) x=2, y=0; j) x=5, y=2  \n6. Resuelve:  \na) ex-2 = e2 (x-1) b) 4x+1 = 22x-3 c) 2x-1 = 8x-3  \nd) 32x+1 - 9x+2 = -702 e) 53x-2 = 625 f) 5x2-x-6 = 1  \ng) 32x-1 - 32x = -54 h) 4x - 2x+2 = 32 i) 5x-2 = 25x-3  \nSol: a) x=0; b) x=􀀟; c) x=4; d) x=1; e) x=2; f) x=-2, x=3; g) x=2; h) x=3; i) x=4  \n7. Resuelve:  \na) 32x+5 = 27x+2 b) 3x+1 + 3x-2 + 3x + 3x-1 = 120 c) 4x + 2x-1 = ~~ ~~12  \nd) 2-x+5 = 8x+3 e) 1 + 2 + 4 + 8 + ... + 2x = 511  \nf) 1 + 3 + 9 + 27 + ... + 3x= 3280  \nh) 1 + 5 + 25 + 125 + ... + 5x= 19531  \nj) 1 + 7 + 49 + 343 + ... + 7x= 19608  \ng) 1 + 4 + 16 + 64 + ... + 4x= 1365  \ni) 1 + 6 + 36 + 216 + ... + 6 x= 55987  \nk) 2x + 2x-1 + 2x+1 + 2x-3 = 29  \nSol: a) x=-1; b) x=3; c) x=-1; d) x=-1; e) x=8; f) x=7; g) x=5; h) x=6; i) x=6; j) x=5; k) x=3  \n8. Resuelve las siguientes ecuaciones:  \na) 3.3x=27 b) 5.3x=405 c) 2x/4=4 d) 42x+1=1/4  \nSol: a) x=2; b) x=4; c) x=4; d) x=-1  \n9. Las siguientes ecuaciones exponenciales tienen soluciones enteras. Hállalas:  \na) 2x2 = 16 1 b) 3x-3 = 812 c)  3x =  1 3 d) 􀂧􀂨  1 􀂷􀂸x =  3 4  \n9 􀂩 3 􀂹  \nSol: a) x=2; b) x=7; c) x=-4; d) x=-1/2  \n10. Resuelve mediante un cambio de variable:  \na) 22x-3.2x-4=0 b) 3x+3x-1-3x-2=11 c) 2x+2-x=65/8  \nSol: a) x=2; b) x=2; c) x=3, x=-3  \nDepartamento de Matemáticas I. E.S. Arroyo de la Miel  \n11. Resuelve las siguientes ecuaciones:  \na) 3x+2 = 729 b) 23x-2 = 16 c) 5x+5x+1 = 750d) 10002+x = 1  \nSol: a) x=4; b) x=2; c) x=3; d) x=-2  \n12. Resuelve:  \na) 22x+1 = 8x-1 b) 3x-1 = 3x2-1 c) 2~~ ~~32xx+21 = ~~ ~~42x5  \nSol: a) x=4; b) x=0, x= 1; c) x=3, x=-2  \n13. Resuelve las siguientes ecuaciones exponenciales:  \na) 2x+1 = 4x b) 3x+2 = 9 c) 4x-1 = 2x+1 d) 25x+2 = 5-x-2 e) 3x-1+3x-3x+1=-45 f) 3x+1-3x-2.3x-1= 12 g) 23x-22x-4=0 h) 32x+1-12.3x+32=0  \nSol: a) x=1; b) x=0; c) x=3; d) x=-2; e) x=3; f) x=2; g) x=1; h) x=0, x=1  \n14. Resuelve lo","cbCaieuwCsi8f0SA","https://ap.wps.com/l/cbCaieuwCsi8f0SA","pdf",850968,9,1,4,"Spanish","es",110,"# Ecuaciones exponenciales\n## Hallar x\n## Simplificar expresiones\n## Resolver ecuaciones\n## Resolver sistemas","[{\"question\":\"Se incluyen soluciones para verificar los resultados?\",\"answer\":\"Sí. En cada bloque de ejercicios se listan soluciones para los distintos apartados, permitiendo comprobar el valor obtenido de x o el de las incógnitas en los sistemas.\"}]","Ecuaciones Exponenciales | PDF",1784012755,6,{"code":4,"msg":32,"data":33},"ok",{"site_id":25,"language":24,"slug":34,"title":13,"keywords":35,"description":14,"schema_data":36,"social_meta":79,"head_meta":81,"extra_data":83,"updated_unix":29},"exponential-equations","",{"@graph":37,"@context":78},[38,54,69],{"@type":39,"itemListElement":40},"BreadcrumbList",[41,45,49,52],{"item":42,"name":43,"@type":44,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":46,"name":47,"@type":44,"position":48},"https://docshare.wps.com/es/document/","Document",2,{"item":50,"name":12,"@type":44,"position":51},"https://docshare.wps.com/es/document/examen/",3,{"item":53,"name":13,"@type":44,"position":22},"https://docshare.wps.com/es/document/exponential-equations/69229/",{"url":53,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":42,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-14","2026-07-14",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72],{"name":73,"@type":74,"acceptedAnswer":75},"Se incluyen soluciones para verificar los resultados?","Question",{"text":76,"@type":77},"Sí. 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