SOLUTION: Find all real solutions x to 4^x - 2^x = 56. Thank you!

Algebra.Com
Question 1032298: Find all real solutions x to 4^x - 2^x = 56.
Thank you!

Answer by ikleyn(52800)   (Show Source): You can put this solution on YOUR website!
.
Find all real solutions x to 4^x - 2^x = 56.
Thank you!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`

Answer. x = 3.

Solution

The standard method of solving equations similar to this one, is to introduce the new variable  y = .

Then your original equation becomes 

 = .

Factor it:

(y-8)*(y+7) = 0.

Only positive root does fit, since y = .
So, y = 8.

Thus you have   = 8,  which implies x = 3.


RELATED QUESTIONS

Find all real solutions x to 4^x - 2^x =... (answered by Alan3354,MathTherapy)
Find all real solutions x to 4^x - 2^x =... (answered by Alan3354)
find all real solutions to the equation x**2=4 x squared =... (answered by stanbon)
Find all real solutions:... (answered by josmiceli)
Find all the real solutions to the equation: |x^(2) -8|=|9-x|-1. Provide exact solutions (answered by josgarithmetic,tommyt3rd)
Find all real solutions to the equation 4^x - 5(2^x) - 24 =... (answered by Alan3354)
x+4/x+2=7/x+2 + 24/x^2-4 Find all the real... (answered by Fombitz)
Find all real solutions to: ln x + ln 2 =... (answered by stanbon)
Find all real solutions: x-5x^1/2+4=0 How would you solve this... (answered by mananth)