which expression is equivalent to $log_5left(\frac{x}{4}\right)^2$?\n$2log_5x + log_54$\n$2log_5x+log_516$\n$…
which expression is equivalent to $log_5left(\frac{x}{4}\right)^2$?\n$2log_5x + log_54$\n$2log_5x+log_516$\n$2log_5x - 2log_54$\n$2log_5x-log_54$
Answer
Explanation:
Step1: Apply power - rule of logarithms
By the power - rule $\log_aM^n=n\log_aM$, we have $\log_5(\frac{x}{4})^2 = 2\log_5\frac{x}{4}$.
Step2: Apply quotient - rule of logarithms
By the quotient - rule $\log_a\frac{M}{N}=\log_aM-\log_aN$, we get $2\log_5\frac{x}{4}=2(\log_5x - \log_54)=2\log_5x-2\log_54$.
Answer:
$2\log_5x - 2\log_54$ (the third option)