Question

1. find $\log_{7}7^{11}$

Explanation:

Step1: Recall Logarithm Power Rule

The power rule of logarithms states that $\log_b(a^n) = n\log_b(a)$. Also, when the base and the argument of a logarithm are the same, i.e., $\log_b(b)=1$.

Step2: Apply the Rule to Given Logarithm

For the expression $\log_7(7^{11})$, using the power rule $\log_b(a^n)=n\log_b(a)$, we have $\log_7(7^{11}) = 11\times\log_7(7)$.
Since $\log_7(7) = 1$ (because the logarithm of a number with the same base is 1), then $11\times\log_7(7)=11\times1 = 11$.

Answer:

11