Question

Find the value of x, if

(i) $3^x=81$

(ii) $2^{x-3}=1$

(iii) $3^{3x-5}=\frac{1}{9^x}$

Answer 1

(i) $3^x=81$

$\Rightarrow 3^x=3^4$

If base are same on both sides, we can equate the exponents.

$\Rightarrow x=4$


(ii) $2^{x-3}=1$

$\Rightarrow 2^{x-3}=2^{\circ }$

If base are same on both sides, we can equate the exponents.


$\Rightarrow x-3=0$

$\Rightarrow x=3$


(iii) $(3{)}^{3x-5}=\frac{1}{9^x}$

$\Rightarrow 3^{3x-5}=\frac{1}{(3^2{)}^x}$

$\Rightarrow 3^{3x-5}=\frac{1}{3^{2x}}$

$\Rightarrow 3^{3x-5}=3^{-2x}$

If base are same on both sides, we can equate the exponents.


$\Rightarrow 3x-5=-2x$

$\Rightarrow 3x+2x=5$

$\Rightarrow 5x=5$

​$\Rightarrow x=1$