By definition of logarithm the value of [tex]$3log _2(9n)[/tex] exists
[tex]$ 6(log _2(3) +3 log _2(n))[/tex].
A logarithm exists as an amount that conveys power to a specified number contains to be raised to create the assigned number.
From the definition of a logarithm, we get
aˣ = b exists the same as x = logₐb
Given: [tex]$3log _2(9n)[/tex]
Simplifying [tex]$log _2(9n) = 2log _2(3) + log _2(n)[/tex]
[tex]$= 3(2log _2(3) + log _2(n))[/tex]
Expanding the equation, we get
[tex]$3(2log _2(3) + log _2(n))[/tex]
[tex]$= 6(log _2(3) +3 log _2(n))[/tex]
[tex]$= 6(log _2(3) +3 log _2(n))[/tex]
Therefore, the value of [tex]$3log _2(9n)[/tex] exists [tex]$ 6(log _2(3) +3 log _2(n))[/tex].
To learn more about logarithm refer to:
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