Question

If \[\frac{3^{5x} \times {81}^2 \times 6561}{3^{2x}} = 3^7\]  then x =

Options

• 3

• -3

• \[\frac{1}{3}\]

• \[- \frac{1}{3}\]

Answer 1

We have to find the value of x provided`(3^(5x )xx 81^2 xx 6561)/(3^2x) = 3^7`

So,

 `(3^(5x)xx 3^(4xx2) xx 3^8)/3^(2x) = 3^7`

By using law of rational exponents we get

 `3^(5x +8 +8-2x)= 3^7`

By equating exponents we get

  `5x +8 +8 -2x =7`

                   ` 3x +16 = 7`

                             `3x = 7-16`

                               `3x=-9`

     `x=(-9)/3`

        `x=-3`