Which expression is equivalent to log sub w the fraction with numerator open paren x squared minus 6 close paren to the 4th power and denominator cube root of x squared plus 8 ?

Use the quotient rule: the logarithm of a fraction is the logarithm of the numerator minus the logarithm of the denominator. Then use the power rule: the exponent 4 comes down in the numerator’s logarithm, and the cube root in the denominator is a power of 1/3. This gives 4 log_w(x² − 6) − 1/3 log_w(x² + 8), which is choice C.

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