Question

find the points of intersection of the following algebraically

y=2^x + 4^x
y=2^x+1 - 4^x+1

I set them equal to each other but not sure if you use logs or what to solve it

Answer 1

xln2+xln4=(x+1)ln2-(x+1)ln4
xln2+xln4=xln2+ln2-xln4-ln4
xln4=ln2-xln4-ln4
(x)2ln4=ln2-ln4
solve for x

Answer 2

that didn't simplify anything... it says that x=ln(1/5)/ln2

Answer 3

anonymous is wrong
you have to take ln of both sides, not the individual terms.

2^x + 4^x = 2^(x+1) - 4^(x+1)
2^x - 2^(x+1) = -4^x - 4^(x+1)
2^x(1 - 2) = -4^x(1+4)
2^x = (5)4^x
2^x = 5(2^(2x))
divide both sides by 2^x
1 = 5(2^x)
1/5 = 2^x
now ln both sides
ln(1/5) = xln2

x = ln(1/5)/ln2