How do you expand #log_bsqrt((xy^4)/z^4)#? Precalculus Properties of Logarithmic Functions Natural Logs 1 Answer Douglas K. Oct 11, 2016 #1/2(ln(x) + 4ln(y) - 4ln(z))/ln(b) # Explanation: #log_bsqrt(xy^4/z^4) = # #lnsqrt((xy^4)/z^4)/ln(b) = # #1/2ln((xy^4)/z^4)/ln(b) = # #1/2(ln(x) + ln(y^4) - ln(z^4))/ln(b) = # #1/2(ln(x) + 4ln(y) - 4ln(z))/ln(b) # Answer link Related questions What is the natural log of e? What is the natural log of 2? How do I do natural logs on a TI-83? How do I find the natural log of a fraction? What is the natural log of 1? What is the natural log of infinity? Can I find the natural log of a negative number? How do I find a natural log without a calculator? How do I find the natural log of a given number by using a calculator? How do I do natural logs on a TI-84? See all questions in Natural Logs Impact of this question 1821 views around the world You can reuse this answer Creative Commons License