Question

find the exact solution, using common logarithms, and a two-decimal-place approximation of the solution 4^x-3(4^-x)=8

Answer 1

\[\Large 4^x-3(4^{-x})=8\]first subtract 8 on both sides \[\Large 4^x-3(4^{-x})-8=0\]I would multiply both sides by 4^x \[\Large 4^{2x}-3-8(4^x) = 0\](think about exponent laws and you'll see how to get it.

Now it's like a quadratic.

Answer 2

im terribly confused as to how i would apply common logarithms to this problem. :(

Answer 3

You could say: Let 4^x=y then you would have :
y^2-8y-3=0
Solve for y using the quadratic formula.
Set each answer equal to 4^x and take the log of both sides.

Answer 4

i ended up with this