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vampirchik [111]
3 years ago
15

Which expression is equivalent to log Subscript w Baseline StartFraction (x squared minus 6) Superscript 4 Baseline Over RootInd

ex 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)

Mathematics
2 answers:
Alex73 [517]3 years ago
7 0

Answer:

Option C on E2020

Step-by-step explanation:

TiliK225 [7]3 years ago
4 0

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)

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