first of all we will see how to solve exponential functions....

if a function is of form  a^f(x) = 1  where a>0 ; a  not equal to 1 ;

                       we can put f(x) = 0.

 

if a function is of form *a^f(x) + *b^f(x) + *c^f(x) = 0 and such that b^2 = a*c we wll convert t^2+t+ = 0 ; where t = (a/b)^f(x) solve for  t  and f(x).

 

 

if a function is of form alpha*a^f(x) + beta*b^f(x) +c = 0 where alpha  beta  c  not equal to zero, and a*b = 1 it will become  alpha*t^2+c*t + beta =  0  where t = a^ f(x).

 

 

if  a function is of form  a^f(x) + b^f(x) = c  and a^2 + b^2 = c  then put f(x)= b-a.

 

 

if a function is of the form  (f(x))^g(x)  = 1 then write it as  10^g(x)logf(x)  = 1

 

 

methods of solving equations .......

 

 

 if a equation is given like this  (x-a)(x-b)(x-c)(x-d) = k  where a<b<c<d  and b-a =d-c ; then write it as x^2-(b+C)x+bc = y

 

 

type (2) if ab=cd then put  y = x+(ab)/x

 

 

type(3)   if a function is of form  2n f(x) = g(x)  that implies g(x)  0 then put

 

f(X) = g^2n(x)

 

 

type (4)  if a function is of form 2n f(x) < g(x)  ; f(x)   0 g(x) > 0 and simply put the function in the form  g(x) < g^2n(x).

 

 

type (5)  if a function is of form  2nf(x) > g(x)  and  g(x)   0 then simply put

 

 

f(x) > g^2n(x) and f(x) 0.

 

 

type (6)  solving an equation containing modulus function......

 

 

 mod (f(x) + g(x)) = mod f(x) + mod  G(x)  will mean  f(x)*g(x) >= 0.

 

 

 

                   i hope these will help u.... self written.........