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If x and y are positive integers and 4(2^x)=2^y what is x in terms of y

Respuesta :

Dividing by [tex]2^x[/tex] gives:

[tex]\frac{2^y}{2^x} = 4 [/tex]

Using basic rules of exponents, we have:

[tex]2^{y-x} = 4 [/tex]

Taking the logarithm with base two gives:

[tex]y-x = 2[/tex]

Then, adding [tex]x-2[/tex] to both sides gives:

[tex]x=y-2[/tex]

Let me know if you have any further questions!