Please solve for x in this logarithmic equation? 4^x + 2^(x+1) = 60

[Cuisine123]

Homework Statement

4^x + 2^(x+1) = 60

Homework Equations

N/A

The Attempt at a Solution

4^x + 2^(x+1) = 60
2^2x + 2^(x+1) = 60

I don't know where to go from there.

 

[Mentallic]

edit: ehild has the correct solution.

 

[ehild]

The Attempt at a Solution

4^x + 2^(x+1) = 60
2^2x + 2^(x+1) = 60

I don't know where to go from there.

You are on the right track. Note that 2^{(x+1)}=2\cdot 2^x and 2^{2x}= (2^x)^2. Then choose 2^x as new variable and solve the resultant second order equation.

ehild