Question #93891

1 Answer
Somebody N.
Jan 24, 2018

#x=2#

Explanation:

Your notation is very ambiguous. I am assuming the equation is
#3^(2x)-2*3^(x+2)+81=0#. If not, then this has all been in vain.
.....................................................................................................................................

#3^(2x)-2*3^(x+2)+81=0#

We can rewrite this using the laws of indices:

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

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

So we have:

#(3^x)^2-2*3^x*3^2+81=0#

Simplify:

#(3^x)^2-18*3^x+81=0#

This is a quadratic in #3^x#

Let #u=3^x#

Then:

#u^2-18u+81=0#

Factor:

#(u-9)^2=0=>u=9#

But:

#u=3^x=>3^x=9#

#3^x=3^2=>x=2#

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