Question

How do you solve `\frac{ 81^ { 3x + 2} }{ 243^ { x } } = 3`?

Answer 1

`x=-1`

Explanation:

To solve this, you can recognize that `81=3^(4)` and `243=3^(5)`, so the equation can be rewritten as

`((3^(4))^(3x+2))/((3^(5))^x)=3`

Next, use properties of exponents to rewrite this as:

`(3^(12x+8))/(3^(5x))=3 <=> 3^(7x+8)=3=3^(1)`

But this means that `7x+8=1` so that `7x=-7` and `x=-1`.