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Help ! Basic logarithmic differentiation question.

  • Thread starter Saterial
  • Start date
  • #1
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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.
 

Answers and Replies

  • #2
118
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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).
 

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