Question

If 81^x=9/3^x, find the value of x.

Answer 1

= > (81)^x = 9/3^x

= > (3^4)^x = 3^2/3^x

= > 3^(4x) = 3^(2-x)

 = > 4x = 2 - x

= > 5x = 2

= > x = 2/5
 

Hope this helps!

Answer 2

Answer:

The value of x is $\frac{2}{5}$.

Step-by-step explanation:

The given equation is

$(81)^x=\frac{9}{3^x}$

It can be written as

$(3^4)^x=\frac{3^2}{3^x}$

$3^{4x}=3^{2-x}$                                 $[\because \frac{a^m}{a^n}=a^{m-n}]$

On comparing both the sides, we get

$4x=2-x$

$4x+x=2$

$5x=2$

$x=\frac{2}{5}$

Therefore the value of x is $\frac{2}{5}$.