How do you solve the exponential equation #9^x=3^(x+27)#?

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Answer 1 · 2017-03-05T17:04:17

We have that

#9^x=3^(x+27)#

#3^(2x)=3^x*3^27#

#3^(2x)/3^x=(3^x*3^27)/3^x#

#3^x=3^27#

#x=27#

Answer 2 · 2017-03-05T18:00:37

#color(red)(x=27#

#9^x=3^(x+27)#

#3^(2x)=3^(x+27)#

multiplyL.H.S. and R.H.S. by #color(red)(1/3#

#color(red)1/cancelcolor(red)3 xx cancelcolor(red)3^(2x)/color(red)1=(cancelcolor(red)3^(x+27))/color(red)1 xx color(red)1/cancelcolor(red)3#

#2x=x+27#

#2x-x=27#

#color(red)(x=27#