SOLUTION: Solve each equation in part analytically. Then solve the associated inequalities in parts (b) and (c). (a)(1/2)^-x=(1/4)^x+1 (b) (1/2)^-1> or = to (1/4)^x+1 (c) (1/2)^-x< or =

Question 744778: Solve each equation in part analytically. Then solve the associated inequalities in parts (b) and (c). (a)(1/2)^-x=(1/4)^x+1 (b) (1/2)^-1> or = to (1/4)^x+1 (c) (1/2)^-x< or =to (1/4)^x+1. Thanks! I am at a lose on how to do this.
Thanks!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Solve each equation in part analytically. Then solve the associated inequalities in parts (b) and (c).
(a)(1/2)^-x=(1/4)^x+1
-----
2^x = (2^-2)^(x+1)
------
2^x = 2^(-2x-2)
------
x = -2x-2
3x = -2
x = -2/3
===================

(b) (1/2)^-1> or = to (1/4)^x+1
----------------
2 or (2^-2)^(x+1)
-----
2 or 2^(-2x-2)
=======================

(c) (1/2)^-x< or =to (1/4)^x+1.
----
2^x or 2^(-2x-2)
===================================
Cheers,
Stan H.

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