Question

1) Solve the following exponential equations: a) 5+ (7).(34x-1) = 40 b) 2 + (4). (e2x+1) = 14 2) Solve the following logarithmic equations: a) log (4x + 1) = log,143 – log (4x - 1) b) 5+ (3). In(2x – 1) = 17 3) Solve the following non-linear system: x + y = 6 x2 + 5x - y = 10 4) y = f(x) = x2 – 4x – 12 is given. a) Find the Vertex b) Find the y-intercept c) Find the x intercept(s), if exist d) Draw the graph

Answer 1

4. О S+ 2 2-(341-1) = чо - 3: 3 е уб-S 23S ч Х Ч 3 чx - 2 3 2 24x- 25 Takia (а both sides, we we get log 3 las (4х1) 173 Тоа е* zb1ae. г ух- - Z 7 3 shoi sbor z1-2h Во ? = it shol = xh go) sibel logs +log 3 log 3 ча 2 2 (аат 1° ob z laab 1 3 чx z la 1 u x = logs хг аг page-1 x ។ 4 - у 2+y: е 2 Хti 27+) Ч: е 21ч — 2 — ! 2 2xt1 - 12 ។ 2x+1 e 2 3 e 2XFI Taking log both sides, wegel loge =1013 2x+12 (73 19a1=х 22 Јаз-

gez log 3-1 2 @ logy thood 143 => (4x+1) = 10g, 143-logo (48-)) seo logy (4x+1) + 1077 (4011)' 2 1099[4*+1) (447)] = 107,143, laparo zlogarb Taking antilog both side, weget (42+1) (42-1) 2143 16X?15142 16 x? 2143+1 2144 x2z quy c2=9 -2 i 6 page x= 3 6 3 5+3.109 (221) =17 3.10g (281) 717-1 = 12 log (2x-1) = 12 = 4 loga zb 2x z e4+1 xzelt ac eb h2 3742 2 xty z > y 26-2 x²+52-4210 -2 put the value of in o wegels ģ

2 3, @ x 2 - 2 2, хао 26, хZ-2L x-intercept ase (60) and (-2,0) Яz -Чx12 at yao Яz -12 Я 2 - Ч-2 2-15 42 9 -9 -12 г - 16 Хz 3, 124-12 - 2 2 -ія 22 ч dz 14-16 -12 - - 12 Хz, 32 2s-20 -12 2 - 2 1 2 0 Хz Хz 2 2 ( X76 y-axis та с It/ 5 аль-к -9 L 1 - х 2 3 6 - ч ter Ist -Ч

x?+ 5X-6+ x =10 x²+622 16 x²+62-1620 x²+82-22-16=0 YOx+8) -2(x+0) zo (3+0(x-2) 20 in o, weget in , wegreb x=2,- put uza y = 6-2 = 4 Ty=y puk xzoo y = 6+0 ( 4 ) y = f(a) z x²-ya-12 azi, b2-4 -(-4) c = -12 Here 2 z -b 2 2 = 2 2 а 2:1 -] so © f(2) 2 4-0 =12 = 420 276 f(2) 2-16 rested (+2,16). 7-intercept (2=0) in ②, wregel 0-0-12 I page 2=0 pub y z y=-12 (0,-12) so © x-intercept, (820) So x²-42120 x²6x+ 22-1220 xca-67+20 4-6) (x-6) (x+220