How do you solve 3^(x-1)= 27/3^x?

Jun 7, 2016

We can use the laws of exponents and simplify to get the answer.
Answer : $x = 2$

Explanation:

${3}^{x - 1} = \frac{27}{{3}^{x}}$

${3}^{x - 1} = {3}^{3} / {3}^{x}$

${3}^{x - 1} = {3}^{3 - x}$

As the bases are equal, we can equate the exponents.

$x - 1 = 3 - x$

$x + x = 3 + 1$

$2 x = 4$

$x = 2$