Question

$(\frac{-2}{3})^{13} * (\frac{-2}{3})^{8} = (\frac{-2}{3})^{-2x+1}$ find x

Answer 1

Hence, the solution of the given equation is x=11.

Given equation is (-2/3)-13 x (3/-2)8 = (-2/3)-2x+1

To find out: The value of x.

We know that, (a/b)m=(a/b)-m Hence, (3/-2)8=(-2/3)-8

So, the given equation becomes,

(-2/3)-13 x (3/-2)8 = (-2/3)-2x+1

We also know that, a mxan=am+n

Hence, the equation becomes,

(-2/3)-13-8=(-2/3)-2x+1

(-2/3)-21=(-2/3)2x+1

Since, the base on both sides is equal, the exponents must also be equal.