MIME-Version: 1.0 Content-Location: file:///C:/11B8C177/log-exp-hw.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solve the following exponential equations, give the exact and the approximate solutions

Solve the following exponential eq= uations, give the exact and the approximate solutions.

 

1.   5e2x =3D 7        =             &nb= sp;                  =           2.   3e -= 2x+1 =3D 6         =    

Exact answer: x =3D ½* LN(<= /span>7/5)        =            Exact answer: x =3D (1 – LN(2)) /2        =            

Approxi= mate:  0.168<= span style=3D'mso-spacerun:yes'>        =             &nb= sp;           Approximate:  0.1534        =             &nb= sp;     

&n= bsp;

3.   4 – e 3x+ 1 =3D 2        =             &nb= sp;            =         4.  2* 10 3x - 2 =3D 5

Exact answer: x =3D (LN(2) = – 1)/3        =         Exact answer: x =3D (LOG(5/2) + 2)/3        =             &nb= sp;       

Approximate: - 0.1023        =                =          Approximate:  0.7993        =             &nb= sp;     

 

5.   6 + 3* 10 1- x =3D 10        =                   =       6.  -7 – 3*10 2x - 1 =3D -24

Exact answer:  <= /span>x =3D 1 – LOG(4/3)        =       Exact answer: x =3D (LOG(17/3)+1)/2        =             &nb= sp;      

Approxi= mate:  0.8750=         =                =          Approximate:   0.8767        =             &nb= sp;    

&n= bsp;

7.   8 =3D 12 – 2e 2- x         =                     =         8. 5*10 2 - 3x + 3 =3D 14

Exact answer: x =3D 2 – LN(<= /span>2)        =              Exact answer: x =3D (2 – LOG( 11/5)) /3        =             &nb= sp;     

Approximate: &nb= sp; 1.307        =             &nb= sp;            Approximate:  0.5525        =             &nb= sp;     

 

 

Solve the following log equations,= give the exact and the approximate solutions.

 

9.  LOG(3x+1) =3D 3/5        =                    =   10.  LN(2 &#= 8211; x) =3D -2/3

Exact answer: x =3D (103/5 – 1)/3        =       Exact answer: x =3D 2 –= e -2/3        =             &nb= sp;           

Approximate:  0.9937        =                    =  Approximate: 1.487        =             &nb= sp;       

 

11.   2LOG(2x –3) =3D 1/3        =                  12.  2 + Log(4 – 2x) =3D -8

Exact answer: x =3D (101/6 + 3)/2        =        Exact answer: x =3D (4 – 10-10)/2         =                =             &nb= sp;       

Approximate:  2.234        =             &nb= sp;          = Approximate: 2.000        =             &nb= sp;       

 

13.  3 –= 5LN(3x +1) =3D -8        =                 = 14.  -3 +5LOG(1 – 2x) =3D 9

Exact answer:  <= /span>x =3D (e11/5 – 1 )/3          =     Exact answer:  x =3D (1 – 10 12/5= )/2         =             &nb= sp;           

Approximate:  2.675        =                     =    Approximate:  -125.1        =             &nb= sp;     

 

15.  2LN(2x – 1) – 3 =3D 5        =                   16.  7 – 2LN(12x+15) =3D23   

Exact answer: x =3D (e4+1)/2        =                Exact answ= er: x =3D (e-8 – 15 )/12        =             &nb= sp;          

Approximate:  27.80        =                      =     Approximate:  -1.250        =                   =