SOLUTION: Hello, Please help me with the following as I am completely stuck on it and google isn't helping me find methods involving a "y" variable. "Given that 2^y = 16^(x – 3) and 3^

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Hello, Please help me with the following as I am completely stuck on it and google isn't helping me find methods involving a "y" variable. "Given that 2^y = 16^(x – 3) and 3^      Log On


   

Question 860090: Hello,
Please help me with the following as I am completely stuck on it and google isn't helping me find methods involving a "y" variable.
"Given that 2^y = 16^(x – 3) and 3^(y+2) = 27^x, find the value of x + y"
Thank you!!
Found 2 solutions by josmiceli, mananth:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+2%5Ey+=+16%5E%28+x-3+%29+
+2%5Ey+=+%28+2%5E4+%29%5E%28x-3+%29+
+2%5Ey+=+2%5E%28+4%2A%28+x-3+%29+%29+
+y+=+4%2A%28+x-3+%29+
(1) +4x+-+y+=+12+
-----------------
+3%5E%28+y%2B2+%29+=+27%5Ex+
+3%5E%28+y%2B2+%29+=+%28+3%5E3+%29%5Ex+
+3%5E%28+y%2B2+%29+=+3%5E3x+
+y+%2B+2+=+3x+
(2) +3x+-+y+=+2+
------------------
Subtract (2) from (1)
(1) +4x+-+y+=+12+
(2) +-3x+%2B+y+=+-2+
+x+=+10+
and
(2) +3%2A10+-+y+=+2+
(2) +30+-+y+=+2+
(2) +y+=+28+
-------------------
check:
+2%5Ey+=+16%5E%28+x-3+%29+
+2%5E28+=+16%5E7+
+2%5E28+=+%28+2%5E4+%29%5E7+
+2%5E28+=+2%5E28+
------------------
You can check other equation

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
2^y = 16^(x – 3) and 3^(y+2) = 27^x
2^(y) = 16^(x – 3)
2%5E%28y%29+=+2%5E%284%28x-3%29%29
y=4(x-3)......................(1)
3%5E%28y%2B2%29+=+27%5Ex
3%5E%28y%2B2%29=3%5E3x
y+2=3x
y-3x=-2......................(2)
substitute y
4(x-3)-3x=-2
4x-12-3x=-2
x=10
y=28