Question

Find x so that [(1/3)^-5×(1/3)^7=(1/3)^2x-1]

Answer 1

The value of x is $\mathbf{\frac{3}{2}}$

Step-by-step explanation:

• Given data

        $\mathbf{\left ( \frac{1}{3} \right )^{-5}\times \left ( \frac{1}{3} \right )^{7}=\left ( \frac{1}{3} \right )^{2x-1}}$

• Exponent will add on multiplication of same base

        $\mathbf{\left ( \frac{1}{3} \right )^{-5+7}=\left ( \frac{1}{3} \right )^{2x-1}}$  

 

        $\mathbf{\left ( \frac{1}{3} \right )^{2}=\left ( \frac{1}{3} \right )^{2x-1}}$

• On comparing the exponent on both side

        2 x -1 = 2

        2 x = 2 +1

        2 x = 3

        So

        $\mathbf{x=\frac{3}{2}}$     Answer