Question

$25 \times 5 {{?x} = 5 {?8}$
​

Answer 1

Answer:

$25\times \:5^x=5^8\quad :\quad x=6$

Step-by-step explanation:

$25\times \:5^x=5^8$

$\gray{\mathrm{Divide\:both\:sides\:by\:}25}$

$\dfrac{25\times \:5^x}{25}=\dfrac{5^8}{25}$

$\gray{\mathrm{Simplify}}$

$5^x=\dfrac{5^8}{25}$

$\black{\mathrm{Simplify\:}\dfrac{5^8}{25}:}$

$\dfrac{5^8}{25}$

$\gray{\mathrm{Factor}\:25:\quad 5^2}$

$=\dfrac{5^8}{5^2}$

$\gray{\mathrm{Cancel\:}\dfrac{5^8}{5^2}:\quad 5^6}$

$=5^6$

$5^x=5^6$

$\gray{\mathrm{If\:}a^{f\left(x\right)}=a^{g\left(x\right)}\mathrm{,\:then\:}f\left(x\right)=g\left(x\right)}$

$x=6$