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JcAlmighty

The answer is n.

If: \(log_x(y^{z}) = z*log_x(y)\)
Then: \(log_b( b^{n}) = n*log_b(b)\)

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

Therefore:
\(log_b( b^{n}) = n*log_b(b) =n*1=n\)

Answer:

 \(log_{b} b^{n}\) = n.

Step-by-step explanation:

Given :  \(log_{b} b^{n}\) , b is any positive number not equal to 1 and n is any number.

To find : Evaluate the expression  \(log_{b} b^{n}\).

Formula used : \(log_{b} x^{y}\). = y ∙ \(log_{b}\)(x) and

\(log_{b}(b) = 1.

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

By logarithm rule :  \(log_{b} x^{y}\). = y ∙ \(log_{b}\)(x).

Then  \(log_{b} b^{n}\) = n∙ \(log_{b}\)(b).

By logarithm rule :  \(log_{b}(b) = 1.

Now, n∙ [tex]log_{b}\)(b) = n.

Therefore,  \(log_{b} b^{n}\) = n.

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