How do you solve the exponential inequality #5^(2x+2)>=25^(2x-3)#?

1 Answer
Apr 14, 2017

Answer:

#x <=4#

Explanation:

Note that #25=5^2#
So #25^(2x-3)=(5^2)^(2x-3)=5^(4x-6)#

Therefore
#color(white)("XXX")5^(2x+2) >= 25^(2x-3)#
is equivalent to
#color(white)("XXX")5^(2x+2) >=5^(4x-6)#

which will be true if
#color(white)("XXX")2x+2 >= 4x-6#

Subtracting #2x# from both sides then adding #6# (to both sides)
#color(white)("XXX")8 >= 2x#

or
#color(white)("XXX")x <=4#