ln(xy^2z^3/w)^2
S soroban Elite Member Joined Jan 28, 2005 Messages 5,586 Apr 5, 2007 #2 Hello, kp8179! Write in "expanded" form: \(\displaystyle \L\:\ln\left(\frac{xy^2z^3}{w}\right)^2\) Click to expand... \(\displaystyle \L\ln\left(\frac{xy^2z^3}{w}\right)^2\) . . \(\displaystyle \L=\:\ln\left(\frac{x^2(y^2)^2(z^3)^2}{w^2}\right)\) . . \(\displaystyle \L=\;\ln\left(\frac{x^2y^4z^6}{w^2}\right)\) . . \(\displaystyle \L= \;\ln\left(x^2y^4z^6\right)\,-\,\ln(w^2)\) . . \(\displaystyle \L= \;\ln(x^2)\,+\,\ln(y^4) \,+\,\ln(z^6)\,-\,\ln(w^2)\) . . \(\displaystyle \L=\;2\cdot\ln(x)\,+\,4\cdot\ln(y)\,+\,6\cdot\ln(z)\,-\,2\cdot\ln(w)\)
Hello, kp8179! Write in "expanded" form: \(\displaystyle \L\:\ln\left(\frac{xy^2z^3}{w}\right)^2\) Click to expand... \(\displaystyle \L\ln\left(\frac{xy^2z^3}{w}\right)^2\) . . \(\displaystyle \L=\:\ln\left(\frac{x^2(y^2)^2(z^3)^2}{w^2}\right)\) . . \(\displaystyle \L=\;\ln\left(\frac{x^2y^4z^6}{w^2}\right)\) . . \(\displaystyle \L= \;\ln\left(x^2y^4z^6\right)\,-\,\ln(w^2)\) . . \(\displaystyle \L= \;\ln(x^2)\,+\,\ln(y^4) \,+\,\ln(z^6)\,-\,\ln(w^2)\) . . \(\displaystyle \L=\;2\cdot\ln(x)\,+\,4\cdot\ln(y)\,+\,6\cdot\ln(z)\,-\,2\cdot\ln(w)\)
