SOLUTION: 4^(3x-2)=6^x I have the solution x=1.1713 to 4 decimal places. I am just not sure what steps I need to take in order to find this solution. Please help! Thank you very much!

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 4^(3x-2)=6^x I have the solution x=1.1713 to 4 decimal places. I am just not sure what steps I need to take in order to find this solution. Please help! Thank you very much!      Log On


   

Question 865373: 4^(3x-2)=6^x
I have the solution x=1.1713 to 4 decimal places.
I am just not sure what steps I need to take in order to find this solution.
Please help!
Thank you very much!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4%5E%283x-2%29=6%5Ex Start with the given equation.


ln%284%5E%283x-2%29%29=ln%286%5Ex%29 Take the natural log of both sides.


%283x-2%29%2Aln%284%29=x%2Aln%286%29 Pull down the exponents.


3x%2Aln%284%29-2%2Aln%284%29=x%2Aln%286%29 Distribute.


3x%2Aln%284%29=x%2Aln%286%29%2B2%2Aln%284%29 Add 2%2Aln%284%29 to both sides.


3x%2Aln%284%29-x%2Aln%286%29=2%2Aln%284%29 Subtract x%2Aln%286%29 from both sides.


x%283%2Aln%284%29-ln%286%29%29=2%2Aln%284%29 Factor out x


x=%282%2Aln%284%29%29%2F%283%2Aln%284%29-ln%286%29%29 Divide both sides by 3%2Aln%284%29-ln%286%29 to isolate x.


x=1.17129021301953 Use a calculator to evaluate the right hand side (RHS)


x=1.1713 Round to 4 decimal places