How do you solve the exponential inequality #8^(x-1)<=32^(3x-2)#?

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Answer 1 · 2018-06-19T07:28:57

#x>=3/4#

#8^(x-1)<=32^(3x-2)#

change the #8 " and "32# to powers of 2

#(2^3)^(x-1)<=(2^5)^(3x-2)#

ie

#2^(3x-1)<=2^(15x-10)#

#=>3x-1<=15x-10#

solve for #x#

#-1+10<=15x-3x#

#9<=12x#

#12x>=9#

#=>x>=9/12#

#x>=3/4#