SOLUTION: 1.1(2.6)^2x = 6(4.4)^x I have to solve for x and I need the exact solution, not a decimal. I am getting really frustrated because everytime I try something, it leads me to a

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 1.1(2.6)^2x = 6(4.4)^x I have to solve for x and I need the exact solution, not a decimal. I am getting really frustrated because everytime I try something, it leads me to a       Log On


   

Question 227316: 1.1(2.6)^2x = 6(4.4)^x
I have to solve for x and I need the exact solution, not a decimal.
I am getting really frustrated because everytime I try something, it leads me to a dead end. Please help?
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
1.1%282.6%29%5E%282x%29+=+6%284.4%29%5Ex

Take the ln of each side:
+ln%281.1%282.6%29%5E%282x%29%29+=+ln%286%284.4%29%5Ex%29+

+ln%281.1%29+%2B+ln%282.6%29%5E%282x%29+=+ln%286%29%2Bln%284.4%29%5Ex+

+ln%281.1%29+%2B+2x%2Aln%282.6%29+=+ln%286%29%2Bx%2Aln%284.4%29+

Get the x terms on the right side, and the NON-x terms on the left side:
2x%2Aln%282.6%29-x%2Aln%284.4%29=+ln%286%29-ln%281.1%29+

Factor out the x on the left side:
x%282%2Aln%282.6%29+-+ln%284.4%29%29+=+ln%286%29+-ln%281.1%29


Divide both sides by 2%2Aln%282.6%29+-+ln%284.4%29:

x=+%28ln%286%29-ln%284.4%29%29%2F%282%2Aln%282.6%29+-+ln%284.4%29%29+

R^2

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus