use the properties of logarithms to expand \\(\\log \\frac{6^z}{x}\\). each logarithm should involve only…
use the properties of logarithms to expand \\(\\log \\frac{6^z}{x}\\). each logarithm should involve only one variable and should not have any exponents or fractions. assume that all variables are positive.
Answer
Explanation:
Step1: Apply Quotient Rule
The quotient rule of logarithms states that $\log_b \frac{M}{N} = \log_b M - \log_b N$. For $\log \frac{6^z}{x}$, we have $M = 6^z$ and $N = x$. So, $\log \frac{6^z}{x}=\log 6^z - \log x$.
Step2: Apply Power Rule
The power rule of logarithms states that $\log_b M^n = n\log_b M$. For $\log 6^z$, using the power rule, we get $z\log 6$. So the expanded form is $z\log 6 - \log x$.
Answer:
$z\log 6 - \log x$