Question

Which of the following is the solution to the equation 25^(z+4)=125

Answer 1

`\bf 25^(z+4)=125~~ \begin{cases} 25=5^2\\ 125=5^3 \end{cases}\implies (5^2)^(z+4)=5^3\implies 5^(2(z+4))=5^3 \\\\\\ \stackrel{\textit{same bases, thus same exponents}}{2(z+4)=3\implies 2z+8=3}\implies 2z=-5\implies z=-\cfrac{5}{2}`