Question

find the exact value of the following logarithmic expression. \\(\log_{e}(e^{11})\\) \\(\log_{e}(e^{11}) = \square\\)

Explanation:

Step1: Recall the logarithm power rule

The power rule of logarithms states that $\log_b(a^c) = c\log_b(a)$. Applying this to $\log_e(e^{11})$, we get $11\log_e(e)$.

Step2: Recall the property of $\log_b(b)$

For any positive number $b
eq1$, $\log_b(b) = 1$. Here, $b = e$, so $\log_e(e)=1$.

Step3: Calculate the final value

Substituting $\log_e(e)=1$ into $11\log_e(e)$, we have $11\times1 = 11$.

Answer:

11