SOLUTION: Hello all! Can someone please help me ASAP! Condense the following... log3 2x+3 log3 4x ( the 3 next to first log is supposed to be next to it but is a subscript same with 3

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Question 142461: Hello all! Can someone please help me ASAP!
Condense the following...
log3 2x+3 log3 4x ( the 3 next to first log is supposed to be next to it but is a subscript same with 3 after the 2nd log)
ln 72x-2 ln 2y
Solve the following Equations...
9^(x+2)=(1/27)^(x+12)
27^(2x+4)=(1/9)^(x-46)
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
log3 (2x+3) log3 (4x) ( the 3 next to first log is supposed to be next to it but is a subscript same with 3 after the 2nd log)
= log3 [(2x+3)(4x)]
= log3 [4x^2+12x]
---------------------------
ln 72x - 2ln 2y
=ln(72x) - ln(2y)^2
=ln(72x) - ln(4y^2)
=ln[72x/4y^2]
= ln[18x/y^2]
-----------------------------
Solve the following Equations...
9^(x+2)=(1/27)^(x+12)
(3^2)^(x+2) = (3^-3)^(x+12)
3^(2x+4) = 3^(-3x-36)
2x+4 = -3x-36
5x = -40
x = -8
---------------
27^(2x+4)=(1/9)^(x-46)
(3^2)^(2x+4) = (3^-2)^(x-46)
3^(2x+8) = 3^(-2x+92)
2x+8 = -2x+92
4x = 84
x = 21
==================
Cheers,
Stan H.