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please someone help me with this! Giving brainliest :)

Please Someone Help Me With This Giving Brainliest class=

Sagot :

danielgeyfman

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!

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