Drewbee0606 Drewbee0606

21-03-2019
Mathematics

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

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jdoe0001 jdoe0001

21-03-2019

[tex]\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}[/tex]

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