How do you solve #(\root[ 3] { 7} ) ^ { 1- 2x } = 7^ { x ^ { 2} }#?

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Answer 1 · 2017-10-26T04:26:47

#x = 1/3, -1#

#root(3)(7)^(1-2x) = 7^(x^2)#

#(7)^((1-2x)/3) =( 7)^(x^2)#

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

#3x^2 + 2x -1 = 0#

#3x^2 +3x -x -1 = 0#

#(3x-1) (x+1) = 0#

#x = 1/3, -1#