Question

Which expression is equivalent to log Subscript w Baseline StartFraction (x squared minus 6) Superscript 4 Baseline Over RootIndex 3 StartRoot x squared + 8 EndRoot EndFraction?
4 log Subscript w Baseline StartFraction x squared Over 1296 EndFraction minus one-third log Subscript w Baseline (2 x + 8)
4 log Subscript w Baseline (x squared minus 6) minus one-third log Subscript w Baseline (x squared + 8)
4 log Subscript w Baseline (X squared minus 6) minus one-third log Subscript w Baseline (x squared + 8)
4 (log Subscript w Baseline x squared minus one-third log Subscript w Baseline (x squared + 8) minus 6)

Answer 1

Answer:

Option C on E2020

Step-by-step explanation:

Answer 2

Answer:

$4log_w (x^2-6)-\frac{1}{3}log_w (x^2+8)$

Step-by-step explanation:

The expression to simplify is given as:

$L= log_w \frac{(x^2-6)^4}{\sqrt[3]{x^2+8} }$

Using the log property $log_a \frac{x}{y}=log_a x-log_a y$, we get

$L=\log_w (x^2-6)^4- \log_w \sqrt[3]{(x^2+8)}$

Now, we know that $\sqrt[3]{x} =(x)^{\frac{1}{3}}$.So,

$\sqrt[3]{(x^2+8)}=(x^2+8)^{\frac{1}{3}}$

Also, property of log is $\log_a x^m=mlog_a x$

Using the above properties, we get

$L=\4\log_w (x^2-6)- \frac{1}{3}\log_w (x^2+8)$

Hence, the given expression is equivalent to $\4\log_w (x^2-6)- \frac{1}{3}\log_w (x^2+8)$