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JcAlmighty
The answer is n.

If: [tex]log_x(y^{z}) = z*log_x(y) [/tex]
Then: [tex]log_b( b^{n}) = n*log_b(b) [/tex]

If: [tex]log_x(y) = \frac{log_z(y)}{log_z(x)} [/tex]
Then: [tex]log_b(b) = \frac{log_z(b)}{log_z(b)} =1[/tex]

Therefore:
[tex]log_b( b^{n}) = n*log_b(b) =n*1=n[/tex]

Answer:

 [tex]log_{b} b^{n}[/tex] = n.

Step-by-step explanation:

Given :  [tex]log_{b} b^{n}[/tex] , b is any positive number not equal to 1 and n is any number.

To find : Evaluate the expression  [tex]log_{b} b^{n}[/tex].

Formula used : [tex]log_{b} x^{y}[/tex]. = y ∙ [tex]log_{b}[/tex](x) and

[tex]log_{b}(b) = 1.

Solution : We have  [tex]log_{b} b^{n}[/tex].

By logarithm rule :  [tex]log_{b} x^{y}[/tex]. = y ∙ [tex]log_{b}[/tex](x).

Then  [tex]log_{b} b^{n}[/tex] = n∙ [tex]log_{b}[/tex](b).

By logarithm rule :  [tex]log_{b}(b) = 1.

Now, n∙ [tex]log_{b}[/tex](b) = n.

Therefore,  [tex]log_{b} b^{n}[/tex] = n.

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