In the real numbers, what is the solution of the equation #8^(2x+1) = 4^(1-x)#?

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Answer 1 · 2017-06-14T07:52:28

#x=-1/8#

#8^((2x+1))=4^((1-x))# can be written as

#(2^3)^((2x+1))=(2^2)^((1-x))#

or #2^(3(2x+1))=2^(2(1-x))#

or #2^(6x+3)=2^(2-2x)#

i.e. #6x+3=2-2x#

or #8x=2-3=-1#

and #x=-1/8#