Question

1. write the expression as a sum and/or difference of logarithms. express exponents as factors. \\(\log_{4}(a^{3}b)\\) \\(\log_{4}(a^{3}b) = \square\\)

Explanation:

Step1: Apply product rule of logarithms

The product rule of logarithms states that $\log_b(MN) = \log_b(M) + \log_b(N)$ for any positive numbers $M$, $N$, and $b>0$, $b
eq1$. Here, $M = a^3$ and $N = b$, and $b = 4$. So we can rewrite $\log_4(a^3b)$ as $\log_4(a^3)+\log_4(b)$.

Step2: Apply power rule of logarithms

The power rule of logarithms states that $\log_b(M^n)=n\log_b(M)$ for any positive number $M$, real number $n$, and $b > 0$, $b
eq1$. Here, $M=a$, $n = 3$, and $b = 4$. So we can rewrite $\log_4(a^3)$ as $3\log_4(a)$.

Answer:

$3\log_{4}(a)+\log_{4}(b)$