SOLUTION: how to find the value of y? 4^y+4^(2*y+1)=1

Question 657728: how to find the value of y?
4^y+4^(2*y+1)=1

Answer by chriswen(106) (Show Source): You can put this solution on YOUR website!
4^y+4^(2*y+1)=1
Simplify the question by making a substitution.
Let x = 4^y

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=17 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.390388203202208, -0.640388203202208. Here's your graph:

0.390388203202208, -0.640388203202208
sub into x = 4^y
logx = ylog4
y = logx/log4
y1 = -0.6785
y2 = invalid (can't log negative numbers)
The answer is approximately -0.6785. If you want exact formula you'll need to use the quadratic formula to solve and leave in exact numbers.

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