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2^x+2^(x+2)=-5y+20
\n" ); document.write( "\"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\":
\n" ); document.write( "2^x = expression-with-y-but-not-x
\n" ); document.write( "or
\n" ); document.write( "expression-with-y-but-not-x = 2^x
\n" ); document.write( "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:
\n" ); document.write( " - 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
\n" ); document.write( "2^x + 2^x*2^2 = -5y + 20
\n" ); document.write( "Since 2^2 = 4 we get:
\n" ); document.write( "2^x + 2^x*4 = -5y + 20
\n" ); document.write( "or
\n" ); document.write( "2^x + 4*2^x = -5y + 20
\n" ); document.write( "And exactly like q + 4q = 5q the left side adds up to:
\n" ); document.write( "5*2^x = -5y + 20
\n" ); document.write( "Now we just divide by 5:
\n" ); document.write( "2^x = -y + 4
\n" ); document.write( "And we're finished. \n" ); document.write( "