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

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) (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:

Take the natural log of both sides of the equation:

so...

Distribute ln(4) and ln(3).

Add ln(4) and subtract 2ln(3) from both sides of the equation:

Factor out x on the left side of the equation and use the fact that blna=lna^b to simplify the right side:

Use the fact that lna+lnb=ln(a*b) and lna-lnb=ln(a/b)to simplify the equation:

Divide both sides by ln(12)

Stick ln(9216) in your calculator=9.128696383.
Stick ln(12) in your calculator=2.48490665.
so

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.

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