SOLUTION: Ok so I have another question - I'm struggling to get log laws and have the question, I appreciate getting the answer but really need to understand what's happening that I'm not gr

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Question 1090804: Ok so I have another question - I'm struggling to get log laws and have the question, I appreciate getting the answer but really need to understand what's happening that I'm not grasping
Express y in terms of x
x=4(3^y) + 3^y - 3(^y+log_3x)
So my thought was to take 4 over to the left so it becomes
x/4 = 3^y + 3^y - 3(^y+log_3x)
Then to get the powers down, use natural log and multiply out brackets
ln(x/4)= yln3 + yln3 - yln3 - log_3xln3
I would think then that yln3 - yln3 would cancel each other out, so
ln(x/4) = yln3 - log_3xln3
This is where my thought process gets stuck as I know log_3 3 is 1 but not sure about what log_3xln3 is telling me
my final answer would be ((x/4)+x)/ln3 = y
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
I am not sure what the "^" means in the expression: 3(^y+log_3x)
Is it 3%5E%28%28y%2Blog%283x%29%29%29 or what?
So we have
x=4%283%5Ey%29+%2B+3%5Ey+-+3%5E%28y%2Blog%283x%29%29
if you divide by 4 here you have to divide each term by 4, not like you did it.
3^y are like terms so you can add them
x=5%283%5Ey%29-+3%5E%28y%2Blog%283x%29%29
we can rearrange it
5%283%5Ey%29=+x+%2B+3%5E%28y%2Blog%283x%29%29
divide both sides by 5
3%5Ey+=+%28x+%2B+3%5E%28y%2Blog%283x%29%29%29%2F5
this is as far as I have time for right now, will continue this later