SOLUTION: i need to find the value of x here and i really need your help... i need the answer today at least before 6-9 in the morning... thanks... (4^(x-1))*(3^(x+2))=12^4

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: i need to find the value of x here and i really need your help... i need the answer today at least before 6-9 in the morning... thanks... (4^(x-1))*(3^(x+2))=12^4      Log On


   

Question 53295: i need to find the value of x here and i really need your help... i need the answer today at least before 6-9 in the morning... thanks...
(4^(x-1))*(3^(x+2))=12^4
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
I answered this one using natural logs earlier today. I hope you're not the same person and I just wasn't clear enough. I will explain myself:
4%5E%28x-1%29%2A3%5E%28x%2B2%29=12%5E4
Take the natural log of both sides of the equation:
ln%284%5E%28x-1%29%2A3%5E%28x%2B2%29%29=ln%2812%5E4%29
ln%28a%2Ab%29=ln%28a%29%2Bln%28b%29so...
ln%284%5E%28x-1%29%29%2Bln%283%5E%28x%2B2%29%29=ln%2812%5E4%29
ln%28a%5Eb%29=bln%28a%29 so...
%28x-1%29ln%284%29%2B%28x%2B2%29ln%283%29=ln%2812%5E4%29
Distribute ln(4) and ln(3).
xln%284%29-ln%284%29%2Bxln%283%29%2B2ln%283%29=ln%2812%5E4%29
Add ln(4) and subtract 2ln(3) from both sides of the equation:

xln%284%29%2Bxln%283%29=ln%2812%5E4%29%2Bln%284%29-2ln%283%29
Factor out x on the left side of the equation and use the fact that blna=lna^b to simplify the right side:
x%28ln%284%29%2Bln%283%29%29=ln%2812%5E4%29%2Bln%284%29-ln%283%5E2%29
Use the fact that lna+lnb=ln(a*b) and lna-lnb=ln(a/b)to simplify the equation:
x%28ln%284%2A3%29%29=ln%28%2812%5E4%2A4%29%2F%283%5E2%29%29
x%28ln%2812%29%29=ln%2820736%2A4%2F9%29
x%28ln%2812%29%29=ln%2882944%2F9%29
xln%2812%29=ln%289216%29
Divide both sides by ln(12)
%28xln%2812%29%29%2F%28ln%2812%29%29=%28ln%289216%29%29%2F%28ln%2812%29%29
x=%28ln%289216%29%29%2F%28ln%2812%29%29
Stick ln(9216) in your calculator=9.128696383.
Stick ln(12) in your calculator=2.48490665.
so
x=9.128696383%2F2.48490665
x=3.673657675
You can verify this with a graphing calculator by finding the intersection between 4^(x-1)*3(x+2) and 12^4.
If you plug your answer into the equation you get:
20736.00006=20736 which is very close. Keep in mind that we had to round off.