How do you solve #(e^3)^(2x) = (e^3)(e^(2x))#?

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Answer 1 · 2016-06-08T14:02:27

#x = 3/4#

#(e^3)^{2x} = e^{3 xx 2x} = e^{6x}#

so

#e^{6x}= e^{4x}e^{2x} = (e^3)(e^{2x})#

then

#(e^{4x}-e^3)e^{2x} =0#

but

#e^{2x} > 0#

so

#e^{4x}=e^3->4x=3->x = 3/4#