Answer:
[tex]n=3[/tex]
Step-by-step explanation:
Note that [tex]2^5*5^2=2^3*2^2*5^2=2^3*(2*5)^2=2^3*10^2[/tex].
Aha! We see a path to the solution!
We now know that our equation is actually [tex]2^3*10^2=2^{n}*10^2[/tex].
We can divide both sides by [tex]10^2[/tex] to get [tex]2^3=2^{n}[/tex].
By inspection or taking the logarithm base 2 of both sides, we see that [tex]3=n[/tex].
So, the answer is [tex]\boxed{n=3}[/tex] and we're done!
