SOLUTION: Suppose the function r is defi ned as follows: r (x) = 4^(2x+1) - 8 Write down D(r) and solve the equation r (x) = 0

Algebra ->  Rational-functions -> SOLUTION: Suppose the function r is defi ned as follows: r (x) = 4^(2x+1) - 8 Write down D(r) and solve the equation r (x) = 0       Log On


   

Question 1143119: Suppose the function r is defi ned as follows:
r (x) = 4^(2x+1) - 8
Write down D(r) and solve the equation r (x) = 0

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
r+%28x%29+=+4%5E%282x%2B1%29+-+8
r+%28x%29+=+%282%5E2%29%5E%282x%2B1%29+-+8
r+%28x%29+=+2%5E%284x%2B2%29+-+8

.....apply exponent rule


%28d%2Fdx%29%282%5E%284x%2B2%29+-+8%29=ln%282%29%284%2A1%2B0%29%2A2%5E%284x%2B2%29
%28d%2Fdx%29%282%5E%284x%2B2%29+-+8%29=ln%282%29%2A4%2A2%5E%284x%2B2%29
%28d%2Fdx%29%282%5E%284x%2B2%29+-+8%29=ln%282%29%2A2%5E2%2A2%5E%284x%2B2%29
%28d%2Fdx%29%282%5E%284x%2B2%29+-+8%29=ln%282%29%2A2%5E%284x%2B2%2B2%29
%28d%2Fdx%29%282%5E%284x%2B2%29+-+8%29=ln%282%29%2A2%5E%284x%2B4%29


solve the equation r+%28x%29+=+0
4%5E%282x%2B1%29+-+8=0
4%5E%282x%2B1%29+=8
2%5E%284x%2B2%29+=2%5E3...if bases same, exponents are same too
4x%2B2+=3
4x=3-2
4x=1
x=1%2F4