How do you solve #e^ { x ^ { 2} } = \frac { e ^ { 15} } { ( e ^ { x } ) ^ { 2} }#?

1 Answer
Jim S
Dec 9, 2017

#x=3 or x=-5#

Explanation:

  • #e^(x^2)=e^15/e^(2x)# #<=>#

#<=># #lne^(x^2)=ln(e^15/e^(2x))# #<=>#

#<=># #x^2=lne^15-lne^(2x)# #<=>#

#<=># #x^2=15lne-2x*lne# #<=>#

#<=># #x^2 = 15-2x# #<=>#

#<=># #x^2+2x-15=0# #<=>#

#<=># #(x-3)(x+5)=0# #<=>#

#<=># #x=3# or #x=-5#

  • Used logarithm properties :
    #lne=1#
    #lne^x=xlne#
    #lnx=y <=> x=e^y#
    #ln(a/b)=lna-lnb#
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