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melomori [17]
2 years ago
5

For any positive number b not equal to 1 and any number or variable n, evaluate the following expression.

Mathematics
2 answers:
kirza4 [7]2 years ago
5 0

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.

Mila [183]2 years ago
5 0
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
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