If #(9^(x-2) * 3^(2x-2))/(27^(x+3)) =81, x=?#

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Answer 1 · 2018-08-11T15:04:35

#x=19#

Given

#9^(x-2) × 3^(2x-2)/(27^(x+3))=81#

Now,we can write, #9^(x-2)=3^(2(x-2))=3^(2x-4)#

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

Now using the above modifications, we can write the entire equation as,

#3^(2x-4)×3^(2x-2)/3^(3x+9)=81#

Or, #3^(2x-4+2x-2-3x-9)=3^4#

Or, #3^(x-15)=3^4#

So, comparing we can write,

#x-15=4#

Or, #x=19#

Answer 2 · 2018-08-11T15:43:09

#x=19#

#9^(x-2)*3^(2x-2)-:27^(x+3)=81#

#:.(3^2)^(x-2)*3^(2x-2)-:(3^3)^(x+3)=3^4#

#:.3^(2x-4)*3^(2x-2)-:3^(3(x+3))=3^4#

#:.(3^(4x-6))/(3^(3x+9))=3^4#

#:.3^(4x-6-3x-9)=3^4#

#:.3^(x-15)=3^4#

#:.x-15=4#

#:.x=15+4#

#:.x=19#