# Question #26c4a

Nov 28, 2017

$x = 6$
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:
${\left({3}^{4}\right)}^{x} = {\left({3}^{3}\right)}^{- x + 14}$

Then, this becomes:
${3}^{4 x} = {3}^{3 \left(- x + 14\right)}$
because exponents of exponents get multiplied.

We can now simplify this by equating just the exponents:
$4 x = 3 \cdot \left(- x + 14\right)$

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