If (9^(x-2) * 3^(2x-2))/(27^(x+3)) =81, x=?9x−2⋅32x−227x+3=81,x=?

2 Answers
Ashley H
Aug 11, 2018

x=19x=19

Explanation:

Given

9^(x-2) × 3^(2x-2)/(27^(x+3))=819x−2×32x−227x+3=81

Now,we can write, 9^(x-2)=3^(2(x-2))=3^(2x-4)9x−2=32(x−2)=32x−4

Also, 27^(x+3)=3^(3(x+3))=3^(3x+9)27x+3=33(x+3)=33x+9

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

3^(2x-4)×3^(2x-2)/3^(3x+9)=8132x−4×32x−233x+9=81

Or, 3^(2x-4+2x-2-3x-9)=3^432x−4+2x−2−3x−9=34

Or, 3^(x-15)=3^43x−15=34

So, comparing we can write,

x-15=4x−15=4

Or, x=19x=19

Barney V.
Aug 11, 2018

x=19x=19

Explanation:

9^(x-2)*3^(2x-2)-:27^(x+3)=819x−2⋅32x−2÷27x+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

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