How do you expand ${log}_{b} \sqrt{\frac{x y^{4}}{z^{4}}}$ $log_bsqrt((xy^4)/z^4)$ ?

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Answer 1 · 2016-10-11T00:32:44

$\frac{1}{2} \frac{ln (x) + 4 ln (y) - 4 ln (z)}{ln (b)}$ $1/2(ln(x) + 4ln(y) - 4ln(z))/ln(b)$

${log}_{b} \sqrt{x \frac{y^{4}}{z^{4}}} =$ $log_bsqrt(xy^4/z^4) =$

$\frac{ln \sqrt{\frac{x y^{4}}{z^{4}}}}{ln (b)} =$ $lnsqrt((xy^4)/z^4)/ln(b) =$

$\frac{1}{2} \frac{ln (\frac{x y^{4}}{z^{4}})}{ln (b)} =$ $1/2ln((xy^4)/z^4)/ln(b) =$

$\frac{1}{2} \frac{ln (x) + ln (y^{4}) - ln (z^{4})}{ln (b)} =$ $1/2(ln(x) + ln(y^4) - ln(z^4))/ln(b) =$

$\frac{1}{2} \frac{ln (x) + 4 ln (y) - 4 ln (z)}{ln (b)}$ $1/2(ln(x) + 4ln(y) - 4ln(z))/ln(b)$

How do you expand log_bsqrt((xy^4)/z^4)logb√xy4z4log_bsqrt((xy^4)/z^4)?