sadie30
sadie30 sadie30
  • 13-02-2017
  • Mathematics
contestada

((81^x-2)/(27^x))=9

Im getting a bit confused with this one, thanks for your help :)

Respuesta :

Zepdrix
Zepdrix Zepdrix
  • 13-02-2017
81, 27 and 9 are all powers of 3.
Let's write them in terms of 3.

81 = 3^4

Therefore we can write, [tex]81^{x-2}=3^{4(x-2)}[/tex]

and since 27 = 3^3 we can write, [tex]27^x=3^{3x}[/tex]

and 9 is 3^2.

So our equation looks like this,[tex]\dfrac{3^{4(x-2)}}{3^{3x}}=3^2[/tex]

Applying our exponent rule, division to subtraction, gives us,[tex]3^{4(x-2)-3x}=3^2[/tex]

And from this point, since the BASES are the same,
we can simply equate the exponents:

4(x-2)-3x = 2

and then solve for x.
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