SOLUTION: I am really struggling to find the answer to this logarithmic equation that we have been set: 6*(3^x)+4*(3^-x)-14=0 Any help would be appreciated, Many thanks, Trevor

Divide through by 2 since all coefficients are even:





Write  as 



Multiply through by  to clear of fractions:



Simplify:







Replace  by 



Swap the second and third term on the left to get
in descending order or powers of 



Factor the left side:



Set each factor = 0








For each solution for u, replace  by 

For , 



Take logs of both side:



Use the principle of logs on the left that]
allows you to move an exponent in front of
the log:



Divide both sides by 



Use your calculator:



For , 



Multiply through by 3 to clear of fractions:



Write  as 



Add exponents on the left:



Write the  on the right as 



Since the bases are both the same, and positive
and not equal to 1, we may equate the
exponents:





So there are two solutions,

 and 

Edwin