Question

log4( ³√ X^2 / y)

Answer 1

\(\large \bf log_4\left(\cfrac{\sqrt[3]{x^2}}{y}\right)\implies log_4\left(\cfrac{x^{\frac{2}{3}}}{y}\right)\implies log_4\left(x^{\frac{2}{3}}\cdot y^{-1}\right)\)

then you could use the 1st rule listed at -> http://www.chilimath.com/algebra/advanced/log/images/rules%20of%20exponents.gif

Answer 2

\[\log_{4}\sqrt[3]{\frac{ X ^{2} }{Y}}\] ???

Answer 3

ohh ahemm well that

Answer 4

\(\bf \large { log_4\left(\sqrt[3]{\cfrac{x^2}{y}}\right)\implies log_4\left(\cfrac{\sqrt[3]{x^2}}{\sqrt[3]{y}}\right)\implies log_4\left(\cfrac{x^{\frac{2}{3}}}{y^{\frac{2}{3}}}\right)
\\ \quad \\
\implies log_4\left(x^{\frac{2}{3}}\cdot y^{-\frac{2}{3}}\right) }\)

same, use that rule 1 listed there

Answer 5

hmmm wait... the y is not square... dohh

Answer 6

\(\large \bf { log_4\left(\sqrt[3]{\cfrac{x^2}{y}}\right)\implies log_4\left(\cfrac{\sqrt[3]{x^2}}{\sqrt[3]{y}}\right)\implies log_4\left(\cfrac{x^{\frac{2}{3}}}{y^{\frac{1}{3}}}\right)
\\ \quad \\
\implies log_4\left(x^{\frac{2}{3}}\cdot y^{-\frac{1}{3}}\right) }\)