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

Algebra.Com
Question 233595: 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

Answer by Edwin McCravy(20065)   (Show Source): You can put this solution on YOUR website!
I am really struggling to find the answer to this logarithmic equation that we have been set:


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

RELATED QUESTIONS

I am really struggling to find the answer to this logarithmic equation that we have been... (answered by Theo)
We have to solve using the eliminaiton or substitution method. I am really struggling... (answered by nerdybill,Earlsdon)
Hello, I have been struggling with this problem for some time and am not sure which rules (answered by scott8148)
I am a nursing student and I am required to take college algebra. I took it on line and... (answered by stanbon)
Find all solutions to the equation. Use a lowercase n to denote an arbitrary integer;... (answered by stanbon)
2.)Why do we have to check the solutions when we solve radical equations? 4.)... (answered by edjones)
Could someone please show me how to find the equation of a line that passes through... (answered by stanbon)
This is the original equation: x=2^-(y-2) What I have to apply to it is the... (answered by jsmallt9)
Hi, I am really struggling with this word problem involving consecutive integers, I have... (answered by josmiceli)