Question

for any positive number b not equal to 1 and any number or variable n, evaluate the following expression.\\(\log_{b}(b^{n}) = \\)\
\\(\bigcirc\\) a. \\(b\\)\
\\(\bigcirc\\) b. \\(n\\)\
\\(\bigcirc\\) c. \\(b^{n}\\)\
\\(\bigcirc\\) d. \\(n^{b}\\)

Explanation:

Step1: Recall Logarithm Definition

The logarithm $\log_b(x)$ is the exponent to which $b$ must be raised to get $x$. So, if $\log_b(x) = y$, then $b^y = x$.

Step2: Apply to Given Expression

For $\log_b(b^n)$, let $y = \log_b(b^n)$. By the definition, $b^y = b^n$. Since the bases are equal and $b>0, b
eq1$, the exponents must be equal. Thus, $y = n$. So $\log_b(b^n) = n$.

Answer:

B. \( n \)