SOLUTION: please help me solve: 2^x+2^(x+2)=-5y+20 solve for 2^x in terms of y

Question 717057: please help me solve:
2^x+2^(x+2)=-5y+20
solve for 2^x in terms of y
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
2^x+2^(x+2)=-5y+20
"solve for 2^x in terms of y" means "use algebra to transform the equation so the 2^x is by itself on one side of the equation with the other side being an expression involving y". In other "words":
2^x = expression-with-y-but-not-x
or
expression-with-y-but-not-x = 2^x

So what are we to do with 2^(x+2)? This is hardest part of this problem. The key is to connect a few "dots":

2^(x+2) has an exponent that is a sum
We have a rule for exponents that tells us when exponents should be added:
Most rules in Math, including this one, work in both directions. So even though we usually use the rule above on an expression that matches the pattern of the left side to rewrite it according to the pattern on the right side, we can also use it in the other direction. For example we would usually use this rule to rewrite x^7*x^3 as x^(7+3). But we can also use it to rewrite x^(7+3) as x^7*x^3

So we can use this rule to rewrite 2^(x+2):
2^x + 2^x*2^2 = -5y + 20
Since 2^2 = 4 we get:
2^x + 2^x*4 = -5y + 20
or
2^x + 4*2^x = -5y + 20

And exactly like q + 4q = 5q the left side adds up to:
5*2^x = -5y + 20
Now we just divide by 5:
2^x = -y + 4
And we're finished.
RELATED QUESTIONS
Please help me solve... (answered by stanbon)

Please help me solve this COLLECT LIKE TERMS: 1) 7y+16-5y 2)... (answered by stanbon)

Please help me solve! {{X+2=13... (answered by Alan3354)

Solve for y in terms of x 3lny = 2 + 3lnx (answered by stanbon)

please help me solve... (answered by Nate)

please help me solve for x: {{{ y= sqrtx+z^2... (answered by Alan3354)

Can someone please help me? Solve for x in terms of k log{subscript 5}x +... (answered by stanbon)

Please help me solve this: {{{ 2/y=x/(x-1) }}} express x in terms of y I need to see (answered by askmemath)

X+y%x-y=1/2. Solve for y in terms of... (answered by Fombitz)