Chapter 4 - Polynomials - 4.1 Exponents and Their Properties - 4.1 Exercise Set - Page 237: 109

$x=13$

Using the laws of exponents, the value of the variable in the given equation $ \dfrac{t^{26}}{t^x}=t^x $ is \begin{array}{l}\require{cancel} t^{26-x}=t^x \\\\ 26-x=x \\\\ -x-x=-26 \\\\ -2x=-26 \\\\ x=\dfrac{-26}{-2} \\\\ x=13 .\end{array}