Help Basic logarithmic differentiation question.

[Saterial]

Homework Statement

Determine the equation of the line that is tangent to y=8^x at the point on the curve x=1/2.

Homework Equations

Differentiation Rules
m=y2-y1/x2-x1

The Attempt at a Solution

y=8^x
dy/dx=8^x(ln8)
=8^0.5(ln8)
=5.9

y=8^x
=8^0.5
=2.8

5.9=y-2.8/x-0.5
5.9x-y-0.15=0 (My answer)

y=(6root2(ln2))x + root2(2-3ln2) (Real Answer)

How does this answer even make sense, I don't know where to go from here.

 

[murmillo]

Hints:
Don't round your answers; leave them the way they are.
ln8 = ln(2^3)=3ln2
root8 = 2root2
You're doing the problem correctly, but you may want to avoid rounding and reduce your expressions (for example, turn all the root8's into 2root2's).