Question

Question #26c4a

Answer 1

`x=6`
See explanation.

Explanation:

I assume you mean the following: `81^x = 27^(-x+14)`
So I notice here that `81=9^2=3^4` and that `27=3^3`.
Let's rewrite the equation as such:
`(3^4)^x = (3^3)^(-x+14)`

Then, this becomes:
`3^(4x) = 3^(3(-x+14))`
because exponents of exponents get multiplied.

We can now simplify this by equating just the exponents:
`4x = 3*(-x+14)`

We now simply solve this equation, so opening up the parentheses and keeping simplifying, we get:
`4x = -3x +42`
i.e.
`7x = 42`
i.e.
`x = 6`